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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 452 · 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.A square garden has an area of 1764 square m. How long is each side (in m)?
  2. 2.What is 31²? =
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 15²? =
  5. 5.A square garden has an area of 400 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 862 (b) 847 (c) 841
  7. 7.Which of these is a perfect square? (a) 1363 (b) 1335 (c) 1296
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √1936? =
  10. 10.What is the smallest whole number by which 20 must be divided to get a perfect square?
  11. 11.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 289 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 24 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 784 (b) 835 (c) 823
  15. 15.What is the smallest whole number by which 640 must be divided to get a perfect square?
  16. 16.What is √484? =
  17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √289? =
  19. 19.What is 63²? =
  20. 20.How many whole numbers lie between 43² and 44²?
  21. 21.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  22. 22.What is the smallest whole number by which 350 must be divided to get a perfect square?
  23. 23.A square garden has an area of 784 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  25. 25.What is 26²? =
  26. 26.How many whole numbers lie between 39² and 40²?
  27. 27.A square garden has an area of 3364 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 126 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 5² and 6²?
  30. 30.Which of these is a perfect square? (a) 579 (b) 618 (c) 576
  31. 31.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 441 (b) 445 (c) 453
  33. 33.A square garden has an area of 1444 square m. How long is each side (in m)?
  34. 34.What is √1600? =
  35. 35.What is √9409? =
  36. 36.What is 21²? =
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √5929? =
  39. 39.How many whole numbers lie between 16² and 17²?
  40. 40.What is √2601? =

Answer key

  1. 42
  2. 961
  3. 529
  4. 225
  5. 20
  6. 841
  7. 1296
  8. 25
  9. 44
  10. 5
  11. 6
  12. 17
  13. 6
  14. 784
  15. 10
  16. 22
  17. 900
  18. 17
  19. 3969
  20. 86
  21. 2
  22. 14
  23. 28
  24. 7
  25. 676
  26. 78
  27. 58
  28. 14
  29. 10
  30. 576
  31. 13
  32. 441
  33. 38
  34. 40
  35. 97
  36. 441
  37. 169
  38. 77
  39. 32
  40. 51

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