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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 190 · 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.Which of these is a perfect square? (a) 1211 (b) 1156 (c) 1199
  2. 2.Which of these is a perfect square? (a) 379 (b) 384 (c) 361
  3. 3.What is √3969? =
  4. 4.Which of these is a perfect square? (a) 324 (b) 329 (c) 332
  5. 5.A square garden has an area of 1089 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 900 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 40² and 41²?
  11. 11.A square garden has an area of 64 square m. How long is each side (in m)?
  12. 12.What is 21²? =
  13. 13.What is √1225? =
  14. 14.How many whole numbers lie between 18² and 19²?
  15. 15.Which of these is a perfect square? (a) 596 (b) 576 (c) 614
  16. 16.What is the smallest whole number by which 162 must be divided to get a perfect square?
  17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 12² and 13²?
  19. 19.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  20. 20.What is √2916? =
  21. 21.Which of these is a perfect square? (a) 1345 (b) 1334 (c) 1296
  22. 22.What is 51²? =
  23. 23.What is 75²? =
  24. 24.A square garden has an area of 3249 square m. How long is each side (in m)?
  25. 25.What is √2025? =
  26. 26.A square garden has an area of 3025 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 2809 square m. How long is each side (in m)?
  28. 28.What is 20²? =
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 3600 square m. How long is each side (in m)?
  31. 31.What is 36²? =
  32. 32.Which of these is a perfect square? (a) 766 (b) 745 (c) 729
  33. 33.What is √1024? =
  34. 34.How many whole numbers lie between 24² and 25²?
  35. 35.A square garden has an area of 144 square m. How long is each side (in m)?
  36. 36.What is √961? =
  37. 37.How many whole numbers lie between 9² and 10²?
  38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 30² and 31²?
  40. 40.What is the smallest whole number by which 350 must be multiplied to get a perfect square?

Answer key

  1. 1156
  2. 361
  3. 63
  4. 324
  5. 33
  6. 30
  7. 2
  8. 49
  9. 121
  10. 80
  11. 8
  12. 441
  13. 35
  14. 36
  15. 576
  16. 2
  17. 784
  18. 24
  19. 3
  20. 54
  21. 1296
  22. 2601
  23. 5625
  24. 57
  25. 45
  26. 55
  27. 53
  28. 400
  29. 25
  30. 60
  31. 1296
  32. 729
  33. 32
  34. 48
  35. 12
  36. 31
  37. 18
  38. 900
  39. 60
  40. 14

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