Numerical inequalities and the number line (mixed practice)

{"questions":[{"content":"Between what integers is the number $\\frac{47}{6}$ enclosed?[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$7$ and $8$","$6$ and $7$","$8$ and $9$","$5$ and $6$"],"answer":[0]}},"step":1,"hints":["Divide $47$ by $6$: $\\frac{47}{6}=7\\frac{5}{6}$.","Since: $7<7\\frac{5}{6}<8$.","Therefore: $7<\\frac{47}{6}<8$."]},{"content":"Between what integers is the number $\\frac{83}{9}$ enclosed?[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$9$ and $10$","$8$ and $9$","$7$ and $8$","$10$ and $11$"],"answer":[0]}},"step":1,"hints":["Divide $83$ by $9$: $\\frac{83}{9}=9\\frac{2}{9}$.","Since: $9<9\\frac{2}{9}<10$.","Therefore: $9<\\frac{83}{9}<10$."]},{"content":"Between what integers is the number $\\frac{65}{8}$ enclosed?[[choice-4]]","widgets":{"choice-4":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$6$ and $7$"],"answer":[0]}},"step":1,"hints":["Divide $65$ by $8$: $\\frac{65}{8}=8\\frac{1}{8}$.","Since: $8<8\\frac{1}{8}<9$.","Therefore: $8<\\frac{65}{8}<9$."]},{"content":"Between what integers is the number $\\frac{92}{11}$ enclosed?[[choice-5]]","widgets":{"choice-5":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$6$ and $7$"],"answer":[0]}},"step":1,"hints":["Divide $92$ by $11$: $\\frac{92}{11}=8\\frac{4}{11}$.","Since: $8<8\\frac{4}{11}<9$.","Therefore: $8<\\frac{92}{11}<9$."]},{"content":"Between what integers is the number $\\frac{59}{7}$ enclosed?[[choice-6]]","widgets":{"choice-6":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$6$ and $7$"],"answer":[0]}},"step":1,"hints":["Divide $59$ by $7$: $\\frac{59}{7}=8\\frac{3}{7}$.","Since: $8<8\\frac{3}{7}<9$.","Therefore: $8<\\frac{59}{7}<9$."]},{"content":"Between what integers is the number $\\frac{74}{9}$ enclosed?[[choice-7]]","widgets":{"choice-7":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$6$ and $7$"],"answer":[0]}},"step":1,"hints":["Divide $74$ by $9$: $\\frac{74}{9}=8\\frac{2}{9}$.","Since: $8<8\\frac{2}{9}<9$.","Therefore: $8<\\frac{74}{9}<9$."]},{"content":"Between what integers is the number $\\frac{101}{12}$ enclosed?[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$10$ and $11$"],"answer":[0]}},"step":1,"hints":["Divide $101$ by $12$: $\\frac{101}{12}=8\\frac{5}{12}$.","Since: $8<8\\frac{5}{12}<9$.","Therefore: $8<\\frac{101}{12}<9$."]},{"content":"Between what integers is the number $\\frac{86}{7}$ enclosed?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["$12$ and $13$","$11$ and $12$","$10$ and $11$","$13$ and $14$"],"answer":[0]}},"step":1,"hints":["Divide $86$ by $7$: $\\frac{86}{7}=12\\frac{2}{7}$.","Since: $12<12\\frac{2}{7}<13$.","Therefore: $12<\\frac{86}{7}<13$."]},{"content":"Between what integers is the number $\\frac{115}{8}$ enclosed?[[choice-10]]","widgets":{"choice-10":{"type":"choice","options":["$14$ and $15$","$13$ and $14$","$12$ and $13$","$15$ and $16$"],"answer":[0]}},"step":1,"hints":["Divide $115$ by $8$: $\\frac{115}{8}=14\\frac{3}{8}$.","Since: $14<14\\frac{3}{8}<15$.","Therefore: $14<\\frac{115}{8}<15$."]},{"content":"Between what integers is the number $\\frac{97}{11}$ enclosed?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["$8$ and $9$","$7$ and $8$","$9$ and $10$","$6$ and $7$"],"answer":[0]}},"step":1,"hints":["Divide $97$ by $11$: $\\frac{97}{11}=8\\frac{9}{11}$.","Since: $8<8\\frac{9}{11}<9$.","Therefore: $8<\\frac{97}{11}<9$."]}]}

{"questions":[{"content":"Which of these intervals does the number $\\frac{5}{9}$ belong to?[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$[0.3;0.4]$","$[0.4;0.5]$","$[0.5;0.6]$","$[0.6;0.7]$"],"answer":[2]}},"step":1,"hints":["Divide $5$ by $9$: $5:9=0.555\\ldots$.","We get: $\\frac{5}{9}\\approx0.556$.","Check which interval $0.556$ falls into: $0.3\\le0.556\\le0.4$ - no; $0.4\\le0.556\\le0.5$ - no; $0.5\\le0.556\\le0.6$ - yes; $0.6\\le0.556\\le0.7$ - no."]},{"content":"Which of these intervals does the number $\\frac{8}{13}$ belong to?[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$[0.5;0.6]$","$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$"],"answer":[1]}},"step":1,"hints":["Divide $8$ by $13$: $8:13=0.615\\ldots$.","We get: $\\frac{8}{13}\\approx0.615$.","Check which interval $0.615$ falls into: $0.5\\le0.615\\le0.6$ - no; $0.6\\le0.615\\le0.7$ - yes; $0.7\\le0.615\\le0.8$ - no; $0.8\\le0.615\\le0.9$ - no."]},{"content":"Which of these intervals does the number $\\frac{4}{7}$ belong to?[[choice-4]]","widgets":{"choice-4":{"type":"choice","options":["$[0.3;0.4]$","$[0.4;0.5]$","$[0.5;0.6]$","$[0.6;0.7]$"],"answer":[2]}},"step":1,"hints":["Divide $4$ by $7$: $4:7=0.571\\ldots$.","We get: $\\frac{4}{7}\\approx0.571$.","Check which interval $0.571$ falls into: $0.3\\le0.571\\le0.4$ - no; $0.4\\le0.571\\le0.5$ - no; $0.5\\le0.571\\le0.6$ - yes; $0.6\\le0.571\\le0.7$ - no."]},{"content":"Which of these intervals does the number $\\frac{11}{15}$ belong to?[[choice-5]]","widgets":{"choice-5":{"type":"choice","options":["$[0.5;0.6]$","$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$"],"answer":[2]}},"step":1,"hints":["Divide $11$ by $15$: $11:15=0.733\\ldots$.","We get: $\\frac{11}{15}\\approx0.733$.","Check which interval $0.733$ falls into: $0.5\\le0.733\\le0.6$ - no; $0.6\\le0.733\\le0.7$ - no; $0.7\\le0.733\\le0.8$ - yes; $0.8\\le0.733\\le0.9$ - no."]},{"content":"Which of these intervals does the number $\\frac{9}{14}$ belong to?[[choice-6]]","widgets":{"choice-6":{"type":"choice","options":["$[0.5;0.6]$","$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$"],"answer":[1]}},"step":1,"hints":["Divide $9$ by $14$: $9:14=0.642\\ldots$.","We get: $\\frac{9}{14}\\approx0.643$.","Check which interval $0.643$ falls into: $0.5\\le0.643\\le0.6$ - no; $0.6\\le0.643\\le0.7$ - yes; $0.7\\le0.643\\le0.8$ - no; $0.8\\le0.643\\le0.9$ - no."]},{"content":"Which of these intervals does the number $\\frac{6}{11}$ belong to?[[choice-7]]","widgets":{"choice-7":{"type":"choice","options":["$[0.3;0.4]$","$[0.4;0.5]$","$[0.5;0.6]$","$[0.6;0.7]$"],"answer":[2]}},"step":1,"hints":["Divide $6$ by $11$: $6:11=0.545\\ldots$.","We get: $\\frac{6}{11}\\approx0.545$.","Check which interval $0.545$ falls into: $0.3\\le0.545\\le0.4$ - no; $0.4\\le0.545\\le0.5$ - no; $0.5\\le0.545\\le0.6$ - yes; $0.6\\le0.545\\le0.7$ - no."]},{"content":"Which of these intervals does the number $\\frac{10}{13}$ belong to?[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$","$[0.9;1.0]$"],"answer":[1]}},"step":1,"hints":["Divide $10$ by $13$: $10:13=0.769\\ldots$.","We get: $\\frac{10}{13}\\approx0.769$.","Check which interval $0.769$ falls into: $0.6\\le0.769\\le0.7$ - no; $0.7\\le0.769\\le0.8$ - yes; $0.8\\le0.769\\le0.9$ - no; $0.9\\le0.769\\le1.0$ - no."]},{"content":"Which of these intervals does the number $\\frac{5}{12}$ belong to?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["$[0.3;0.4]$","$[0.4;0.5]$","$[0.5;0.6]$","$[0.6;0.7]$"],"answer":[1]}},"step":1,"hints":["Divide $5$ by $12$: $5:12=0.416\\ldots$.","We get: $\\frac{5}{12}\\approx0.417$.","Check which interval $0.417$ falls into: $0.3\\le0.417\\le0.4$ - no; $0.4\\le0.417\\le0.5$ - yes; $0.5\\le0.417\\le0.6$ - no; $0.6\\le0.417\\le0.7$ - no."]},{"content":"Which of these intervals does the number $\\frac{8}{9}$ belong to?[[choice-10]]","widgets":{"choice-10":{"type":"choice","options":["$[0.5;0.6]$","$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$"],"answer":[3]}},"step":1,"hints":["Divide $8$ by $9$: $8:9=0.888\\ldots$.","We get: $\\frac{8}{9}\\approx0.889$.","Check which interval $0.889$ falls into: $0.5\\le0.889\\le0.6$ - no; $0.6\\le0.889\\le0.7$ - no; $0.7\\le0.889\\le0.8$ - no; $0.8\\le0.889\\le0.9$ - yes."]},{"content":"Which of these intervals does the number $\\frac{7}{8}$ belong to?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["$[0.6;0.7]$","$[0.7;0.8]$","$[0.8;0.9]$","$[0.9;1.0]$"],"answer":[2]}},"step":1,"hints":["Divide $7$ by $8$: $7:8=0.875$.","We get: $\\frac{7}{8}=0.875$.","Check which interval $0.875$ falls into: $0.6\\le0.875\\le0.7$ - no; $0.7\\le0.875\\le0.8$ - no; $0.8\\le0.875\\le0.9$ - yes; $0.9\\le0.875\\le1.0$ - no."]}]}

{"questions":[{"content":"Which of the numbers $\\frac{53}{8}$, $\\frac{59}{8}$, $\\frac{66}{8}$ and $\\frac{68}{8}$ belongs to the segment $[7;8]$?[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$\\frac{53}{8}$","$\\frac{59}{8}$","$\\frac{66}{8}$","$\\frac{68}{8}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $8$: $7=\\frac{56}{8}$, $8=\\frac{64}{8}$.","Check each number: $\\frac{53}{8}<\\frac{56}{8}$ - does not belong; $\\frac{56}{8}\\le\\frac{59}{8}\\le\\frac{64}{8}$ - belongs; $\\frac{66}{8}>\\frac{64}{8}$ - does not belong; $\\frac{68}{8}>\\frac{64}{8}$ - does not belong."]},{"content":"Which of the numbers $\\frac{41}{6}$, $\\frac{47}{6}$, $\\frac{50}{6}$ and $\\frac{52}{6}$ belongs to the segment $[7;8]$?[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$\\frac{41}{6}$","$\\frac{47}{6}$","$\\frac{50}{6}$","$\\frac{52}{6}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $6$: $7=\\frac{42}{6}$, $8=\\frac{48}{6}$.","Check each number: $\\frac{41}{6}<\\frac{42}{6}$ - does not belong; $\\frac{42}{6}\\le\\frac{47}{6}\\le\\frac{48}{6}$ - belongs; $\\frac{50}{6}>\\frac{48}{6}$ - does not belong; $\\frac{52}{6}>\\frac{48}{6}$ - does not belong."]},{"content":"Which of the numbers $\\frac{31}{5}$, $\\frac{36}{5}$, $\\frac{41}{5}$ and $\\frac{44}{5}$ belongs to the segment $[7;8]$?[[choice-4]]","widgets":{"choice-4":{"type":"choice","options":["$\\frac{31}{5}$","$\\frac{36}{5}$","$\\frac{41}{5}$","$\\frac{44}{5}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $5$: $7=\\frac{35}{5}$, $8=\\frac{40}{5}$.","Check each number: $\\frac{31}{5}<\\frac{35}{5}$ - does not belong; $\\frac{35}{5}\\le\\frac{36}{5}\\le\\frac{40}{5}$ - belongs; $\\frac{41}{5}>\\frac{40}{5}$ - does not belong; $\\frac{44}{5}>\\frac{40}{5}$ - does not belong."]},{"content":"Which of the numbers $\\frac{25}{4}$, $\\frac{30}{4}$, $\\frac{33}{4}$ and $\\frac{35}{4}$ belongs to the segment $[7;8]$?[[choice-5]]","widgets":{"choice-5":{"type":"choice","options":["$\\frac{25}{4}$","$\\frac{30}{4}$","$\\frac{33}{4}$","$\\frac{35}{4}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $4$: $7=\\frac{28}{4}$, $8=\\frac{32}{4}$.","Check each number: $\\frac{25}{4}<\\frac{28}{4}$ - does not belong; $\\frac{28}{4}\\le\\frac{30}{4}\\le\\frac{32}{4}$ - belongs; $\\frac{33}{4}>\\frac{32}{4}$ - does not belong; $\\frac{35}{4}>\\frac{32}{4}$ - does not belong."]},{"content":"Which of the numbers $\\frac{58}{9}$, $\\frac{67}{9}$, $\\frac{74}{9}$ and $\\frac{76}{9}$ belongs to the segment $[7;8]$?[[choice-6]]","widgets":{"choice-6":{"type":"choice","options":["$\\frac{58}{9}$","$\\frac{67}{9}$","$\\frac{74}{9}$","$\\frac{76}{9}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $9$: $7=\\frac{63}{9}$, $8=\\frac{72}{9}$.","Check each number: $\\frac{58}{9}<\\frac{63}{9}$ - does not belong; $\\frac{63}{9}\\le\\frac{67}{9}\\le\\frac{72}{9}$ - belongs; $\\frac{74}{9}>\\frac{72}{9}$ - does not belong; $\\frac{76}{9}>\\frac{72}{9}$ - does not belong."]},{"content":"Which of the numbers $\\frac{47}{7}$, $\\frac{52}{7}$, $\\frac{57}{7}$ and $\\frac{60}{7}$ belongs to the segment $[7;8]$?[[choice-7]]","widgets":{"choice-7":{"type":"choice","options":["$\\frac{47}{7}$","$\\frac{52}{7}$","$\\frac{57}{7}$","$\\frac{60}{7}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $7$: $7=\\frac{49}{7}$, $8=\\frac{56}{7}$.","Check each number: $\\frac{47}{7}<\\frac{49}{7}$ - does not belong; $\\frac{49}{7}\\le\\frac{52}{7}\\le\\frac{56}{7}$ - belongs; $\\frac{57}{7}>\\frac{56}{7}$ - does not belong; $\\frac{60}{7}>\\frac{56}{7}$ - does not belong."]},{"content":"Which of the numbers $\\frac{69}{10}$, $\\frac{77}{10}$, $\\frac{83}{10}$ and $\\frac{85}{10}$ belongs to the segment $[7;8]$?[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$\\frac{69}{10}$","$\\frac{77}{10}$","$\\frac{83}{10}$","$\\frac{85}{10}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $10$: $7=\\frac{70}{10}$, $8=\\frac{80}{10}$.","Check each number: $\\frac{69}{10}<\\frac{70}{10}$ - does not belong; $\\frac{70}{10}\\le\\frac{77}{10}\\le\\frac{80}{10}$ - belongs; $\\frac{83}{10}>\\frac{80}{10}$ - does not belong; $\\frac{85}{10}>\\frac{80}{10}$ - does not belong."]},{"content":"Which of the numbers $\\frac{83}{12}$, $\\frac{91}{12}$, $\\frac{98}{12}$ and $\\frac{101}{12}$ belongs to the segment $[7;8]$?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["$\\frac{83}{12}$","$\\frac{91}{12}$","$\\frac{98}{12}$","$\\frac{101}{12}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $12$: $7=\\frac{84}{12}$, $8=\\frac{96}{12}$.","Check each number: $\\frac{83}{12}<\\frac{84}{12}$ - does not belong; $\\frac{84}{12}\\le\\frac{91}{12}\\le\\frac{96}{12}$ - belongs; $\\frac{98}{12}>\\frac{96}{12}$ - does not belong; $\\frac{101}{12}>\\frac{96}{12}$ - does not belong."]},{"content":"Which of the numbers $\\frac{61}{9}$, $\\frac{68}{9}$, $\\frac{75}{9}$ and $\\frac{79}{9}$ belongs to the segment $[7;8]$?[[choice-10]]","widgets":{"choice-10":{"type":"choice","options":["$\\frac{61}{9}$","$\\frac{68}{9}$","$\\frac{75}{9}$","$\\frac{79}{9}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $9$: $7=\\frac{63}{9}$, $8=\\frac{72}{9}$.","Check each number: $\\frac{61}{9}<\\frac{63}{9}$ - does not belong; $\\frac{63}{9}\\le\\frac{68}{9}\\le\\frac{72}{9}$ - belongs; $\\frac{75}{9}>\\frac{72}{9}$ - does not belong; $\\frac{79}{9}>\\frac{72}{9}$ - does not belong."]},{"content":"Which of the numbers $\\frac{39}{6}$, $\\frac{46}{6}$, $\\frac{50}{6}$ and $\\frac{54}{6}$ belongs to the segment $[7;8]$?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["$\\frac{39}{6}$","$\\frac{46}{6}$","$\\frac{50}{6}$","$\\frac{54}{6}$"],"answer":[1]}},"step":1,"hints":["Convert the ends of the segment into fractions with the denominator $6$: $7=\\frac{42}{6}$, $8=\\frac{48}{6}$.","Check each number: $\\frac{39}{6}<\\frac{42}{6}$ - does not belong; $\\frac{42}{6}\\le\\frac{46}{6}\\le\\frac{48}{6}$ - belongs; $\\frac{50}{6}>\\frac{48}{6}$ - does not belong; $\\frac{54}{6}>\\frac{48}{6}$ - does not belong."]}]}

{"questions":[{"content":"Between what numbers is the number $\\sqrt{15}$ enclosed?[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$2$ and $3$","$3$ and $4$","$4$ and $5$","$1$ and $2$"],"answer":[1]}},"step":1,"hints":["$3^2=9$, $4^2=16$.","$9<15<16$.","Therefore: $3<\\sqrt{15}<4$."]},{"content":"Between what numbers is the number $\\sqrt{50}$ enclosed?[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$5$ and $6$","$6$ and $7$","$7$ and $8$","$4$ and $5$"],"answer":[2]}},"step":1,"hints":["$7^2=49$, $8^2=64$.","$49<50<64$.","Therefore: $7<\\sqrt{50}<8$."]},{"content":"Between what numbers is the number $\\sqrt{10}$ enclosed?[[choice-4]]","widgets":{"choice-4":{"type":"choice","options":["$1$ and $2$","$2$ and $3$","$3$ and $4$","$4$ and $5$"],"answer":[2]}},"step":1,"hints":["$3^2=9$, $4^2=16$.","$9<10<16$.","Therefore: $3<\\sqrt{10}<4$."]},{"content":"Between what numbers is the number $\\sqrt{65}$ enclosed?[[choice-5]]","widgets":{"choice-5":{"type":"choice","options":["$6$ and $7$","$7$ and $8$","$8$ and $9$","$5$ and $6$"],"answer":[2]}},"step":1,"hints":["$8^2=64$, $9^2=81$.","$64<65<81$.","Therefore: $8<\\sqrt{65}<9$."]},{"content":"Between what numbers is the number $\\sqrt{34}$ enclosed?[[choice-6]]","widgets":{"choice-6":{"type":"choice","options":["$4$ and $5$","$5$ and $6$","$6$ and $7$","$3$ and $4$"],"answer":[1]}},"step":1,"hints":["$5^2=25$, $6^2=36$.","$25<34<36$.","Therefore: $5<\\sqrt{34}<6$."]},{"content":"Between what numbers is the number $\\sqrt{80}$ enclosed?[[choice-7]]","widgets":{"choice-7":{"type":"choice","options":["$7$ and $8$","$8$ and $9$","$9$ and $10$","$6$ and $7$"],"answer":[1]}},"step":1,"hints":["$8^2=64$, $9^2=81$.","$64<80<81$.","Therefore: $8<\\sqrt{80}<9$."]},{"content":"Between what numbers is the number $\\sqrt{18}$ enclosed?[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$3$ and $4$","$4$ and $5$","$5$ and $6$","$2$ and $3$"],"answer":[1]}},"step":1,"hints":["$4^2=16$, $5^2=25$.","$16<18<25$.","Therefore: $4<\\sqrt{18}<5$."]},{"content":"Between what numbers is the number $\\sqrt{99}$ enclosed?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["$8$ and $9$","$9$ and $10$","$10$ and $11$","$7$ and $8$"],"answer":[1]}},"step":1,"hints":["$9^2=81$, $10^2=100$.","$81<99<100$.","Therefore: $9<\\sqrt{99}<10$."]},{"content":"Between what numbers is the number $\\sqrt{23}$ enclosed?[[choice-10]]","widgets":{"choice-10":{"type":"choice","options":["$3$ and $4$","$4$ and $5$","$5$ and $6$","$2$ and $3$"],"answer":[1]}},"step":1,"hints":["$4^2=16$, $5^2=25$.","$16<23<25$.","Therefore: $4<\\sqrt{23}<5$."]},{"content":"Between what numbers is the number $\\sqrt{72}$ enclosed?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["$7$ and $8$","$8$ and $9$","$9$ and $10$","$6$ and $7$"],"answer":[1]}},"step":1,"hints":["$8^2=64$, $9^2=81$.","$64<72<81$.","Therefore: $8<\\sqrt{72}<9$."]}]}

{"questions":[{"content":"Which of the numbers $\\sqrt{3}$, $\\sqrt{5}$, $\\sqrt{20}$ and $\\sqrt{30}$ belongs to the interval $[3;5]$?[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$\\sqrt{3}$","$\\sqrt{5}$","$\\sqrt{20}$","$\\sqrt{30}$"],"answer":[2]}},"step":1,"hints":["$3=\\sqrt{9}$, $5=\\sqrt{25}$.","$\\sqrt{20}\\approx4.47$ - belongs to the gap."]},{"content":"Which of the numbers $\\sqrt{2}$, $\\sqrt{8}$, $\\sqrt{18}$ and $\\sqrt{27}$ belongs to the interval $[2;4]$?[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$\\sqrt{2}$","$\\sqrt{8}$","$\\sqrt{18}$","$\\sqrt{27}$"],"answer":[1]}},"step":1,"hints":["$2=\\sqrt{4}$, $4=\\sqrt{16}$.","$\\sqrt{8}\\approx2.83$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{2}$, $\\sqrt{5}$, $\\sqrt{30}$ and $\\sqrt{60}$ belongs to the interval $[3;6]$?[[choice-4]]","widgets":{"choice-4":{"type":"choice","options":["$\\sqrt{2}$","$\\sqrt{5}$","$\\sqrt{30}$","$\\sqrt{60}$"],"answer":[2]}},"step":1,"hints":["$3=\\sqrt{9}$, $6=\\sqrt{36}$.","$\\sqrt{30}\\approx5.48$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{12}$, $\\sqrt{10}$, $\\sqrt{45}$ and $\\sqrt{80}$ belongs to the interval $[4;7]$?[[choice-5]]","widgets":{"choice-5":{"type":"choice","options":["$\\sqrt{12}$","$\\sqrt{10}$","$\\sqrt{45}$","$\\sqrt{80}$"],"answer":[2]}},"step":1,"hints":["$4=\\sqrt{16}$, $7=\\sqrt{49}$.","$\\sqrt{45}\\approx6.71$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{5}$, $\\sqrt{2}$, $\\sqrt{35}$ and $\\sqrt{63}$ belongs to the interval $[3;7]$?[[choice-6]]","widgets":{"choice-6":{"type":"choice","options":["$\\sqrt{5}$","$\\sqrt{2}$","$\\sqrt{35}$","$\\sqrt{63}$"],"answer":[2]}},"step":1,"hints":["$3=\\sqrt{9}$, $7=\\sqrt{49}$.","$\\sqrt{35}\\approx5.92$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{2}$, $\\sqrt{18}$, $\\sqrt{50}$ and $\\sqrt{54}$ belongs to the interval $[3;6]$?[[choice-7]]","widgets":{"choice-7":{"type":"choice","options":["$\\sqrt{2}$","$\\sqrt{18}$","$\\sqrt{50}$","$\\sqrt{54}$"],"answer":[1]}},"step":1,"hints":["$3=\\sqrt{9}$, $6=\\sqrt{36}$.","$\\sqrt{18}\\approx4.24$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{11}$, $\\sqrt{24}$, $\\sqrt{10}$ and $\\sqrt{55}$ belongs to the interval $[4;7]$?[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$\\sqrt{11}$","$\\sqrt{24}$","$\\sqrt{10}$","$\\sqrt{55}$"],"answer":[1]}},"step":1,"hints":["$4=\\sqrt{16}$, $7=\\sqrt{49}$.","$\\sqrt{24}\\approx4.90$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{7}$, $\\sqrt{13}$, $\\sqrt{2}$ and $\\sqrt{42}$ belongs to the interval $[3;6]$?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["$\\sqrt{7}$","$\\sqrt{13}$","$\\sqrt{2}$","$\\sqrt{42}$"],"answer":[1]}},"step":1,"hints":["$3=\\sqrt{9}$, $6=\\sqrt{36}$.","$\\sqrt{13}\\approx3.61$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{17}$, $\\sqrt{26}$, $\\sqrt{38}$ and $\\sqrt{52}$ belongs to the interval $[5;7]$?[[choice-10]]","widgets":{"choice-10":{"type":"choice","options":["$\\sqrt{17}$","$\\sqrt{26}$","$\\sqrt{38}$","$\\sqrt{52}$"],"answer":[1]}},"step":1,"hints":["$5=\\sqrt{25}$, $7=\\sqrt{49}$.","$\\sqrt{26}\\approx5.10$ - belongs to."]},{"content":"Which of the numbers $\\sqrt{9}$, $\\sqrt{10}$, $\\sqrt{36}$ and $\\sqrt{60}$ belongs to the interval $[4;7]$?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["$\\sqrt{9}$","$\\sqrt{10}$","$\\sqrt{36}$","$\\sqrt{60}$"],"answer":[2]}},"step":1,"hints":["$4=\\sqrt{16}$, $7=\\sqrt{49}$.","$\\sqrt{36}=6$ - belongs to the gap."]}]}