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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 277 · 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.What is 52²? =
  2. 2.What is 99²? =
  3. 3.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  4. 4.A square garden has an area of 225 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 320 (b) 312 (c) 289
  6. 6.What is √400? =
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 83²? =
  9. 9.Which of these is a perfect square? (a) 816 (b) 784 (c) 806
  10. 10.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  11. 11.What is the smallest whole number by which 243 must be divided to get a perfect square?
  12. 12.What is the smallest whole number by which 90 must be divided to get a perfect square?
  13. 13.What is 34²? =
  14. 14.A square garden has an area of 1521 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 1296 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 12² and 13²?
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √7921? =
  20. 20.What is 27²? =
  21. 21.How many whole numbers lie between 47² and 48²?
  22. 22.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 44 must be divided to get a perfect square?
  24. 24.A square garden has an area of 1444 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 14² and 15²?
  26. 26.Which of these is a perfect square? (a) 1198 (b) 1156 (c) 1215
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √7396? =
  30. 30.Which of these is a perfect square? (a) 1352 (b) 1296 (c) 1334
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 38² and 39²?
  33. 33.What is the smallest whole number by which 686 must be divided to get a perfect square?
  34. 34.What is √1225? =
  35. 35.A square garden has an area of 121 square m. How long is each side (in m)?
  36. 36.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  37. 37.What is 66²? =
  38. 38.What is √2601? =
  39. 39.What is 77²? =
  40. 40.What is the smallest whole number by which 56 must be divided to get a perfect square?

Answer key

  1. 2704
  2. 9801
  3. 2
  4. 15
  5. 289
  6. 20
  7. 441
  8. 6889
  9. 784
  10. 2
  11. 3
  12. 10
  13. 1156
  14. 39
  15. 36
  16. 24
  17. 49
  18. 529
  19. 89
  20. 729
  21. 94
  22. 3
  23. 11
  24. 38
  25. 28
  26. 1156
  27. 361
  28. 169
  29. 86
  30. 1296
  31. 64
  32. 76
  33. 14
  34. 35
  35. 11
  36. 2
  37. 4356
  38. 51
  39. 5929
  40. 14

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