← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 113 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.How many whole numbers lie between 45² and 46²?
  2. 2.How many whole numbers lie between 6² and 7²?
  3. 3.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  4. 4.How many whole numbers lie between 12² and 13²?
  5. 5.A square garden has an area of 2500 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 7² and 8²?
  7. 7.What is √144? =
  8. 8.What is √1369? =
  9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 1936 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 1444 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 278 (b) 256 (c) 285
  13. 13.Which of these is a perfect square? (a) 956 (b) 900 (c) 913
  14. 14.What is the smallest whole number by which 54 must be divided to get a perfect square?
  15. 15.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  16. 16.How many whole numbers lie between 18² and 19²?
  17. 17.What is 24²? =
  18. 18.Which of these is a perfect square? (a) 1537 (b) 1521 (c) 1570
  19. 19.A square garden has an area of 100 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √6084? =
  23. 23.What is 70²? =
  24. 24.How many whole numbers lie between 24² and 25²?
  25. 25.How many whole numbers lie between 5² and 6²?
  26. 26.What is √9409? =
  27. 27.What is 52²? =
  28. 28.Which of these is a perfect square? (a) 169 (b) 173 (c) 194
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 891 must be divided to get a perfect square?
  31. 31.A square garden has an area of 49 square m. How long is each side (in m)?
  32. 32.What is 21²? =
  33. 33.Which of these is a perfect square? (a) 1164 (b) 1167 (c) 1156
  34. 34.What is √5476? =
  35. 35.A square garden has an area of 2025 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 17² and 18²?
  37. 37.How many whole numbers lie between 14² and 15²?
  38. 38.Which of these is a perfect square? (a) 206 (b) 196 (c) 209
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 32 must be multiplied to get a perfect square?

Answer key

  1. 90
  2. 12
  3. 14
  4. 24
  5. 50
  6. 14
  7. 12
  8. 37
  9. 225
  10. 44
  11. 38
  12. 256
  13. 900
  14. 6
  15. 10
  16. 36
  17. 576
  18. 1521
  19. 10
  20. 15
  21. 196
  22. 78
  23. 4900
  24. 48
  25. 10
  26. 97
  27. 2704
  28. 169
  29. 121
  30. 11
  31. 7
  32. 441
  33. 1156
  34. 74
  35. 45
  36. 34
  37. 28
  38. 196
  39. 25
  40. 2

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets