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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 144 · 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) 621 (b) 577 (c) 576
  2. 2.What is 70²? =
  3. 3.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  4. 4.What is √900? =
  5. 5.What is the smallest whole number by which 12 must be divided to get a perfect square?
  6. 6.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  7. 7.A square garden has an area of 1764 square m. How long is each side (in m)?
  8. 8.How many whole numbers lie between 40² and 41²?
  9. 9.What is the smallest whole number by which 735 must be divided to get a perfect square?
  10. 10.What is the smallest whole number by which 320 must be divided to get a perfect square?
  11. 11.How many whole numbers lie between 9² and 10²?
  12. 12.What is √3364? =
  13. 13.What is 19²? =
  14. 14.What is √2304? =
  15. 15.What is 20²? =
  16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 15²? =
  18. 18.A square garden has an area of 400 square m. How long is each side (in m)?
  19. 19.Which of these is a perfect square? (a) 745 (b) 735 (c) 729
  20. 20.What is √729? =
  21. 21.Which of these is a perfect square? (a) 784 (b) 828 (c) 795
  22. 22.How many whole numbers lie between 36² and 37²?
  23. 23.A square garden has an area of 576 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 72 must be divided to get a perfect square?
  25. 25.What is the smallest whole number by which 539 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 714 (b) 676 (c) 678
  27. 27.A square garden has an area of 144 square m. How long is each side (in m)?
  28. 28.What is 23²? =
  29. 29.What is 54²? =
  30. 30.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  31. 31.What is √5041? =
  32. 32.What is 71²? =
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 2401 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  36. 36.A square garden has an area of 900 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 43² and 44²?
  38. 38.How many whole numbers lie between 19² and 20²?
  39. 39.Which of these is a perfect square? (a) 144 (b) 156 (c) 161
  40. 40.What is √7921? =

Answer key

  1. 576
  2. 4900
  3. 11
  4. 30
  5. 3
  6. 2
  7. 42
  8. 80
  9. 15
  10. 5
  11. 18
  12. 58
  13. 361
  14. 48
  15. 400
  16. 576
  17. 225
  18. 20
  19. 729
  20. 27
  21. 784
  22. 72
  23. 24
  24. 2
  25. 11
  26. 676
  27. 12
  28. 529
  29. 2916
  30. 14
  31. 71
  32. 5041
  33. 529
  34. 49
  35. 3
  36. 30
  37. 86
  38. 38
  39. 144
  40. 89

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