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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 227 · 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 20² and 21²?
  2. 2.A square garden has an area of 576 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 1024 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 663 (b) 674 (c) 625
  5. 5.What is √9025? =
  6. 6.What is √2304? =
  7. 7.A square garden has an area of 289 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 48 must be divided to get a perfect square?
  9. 9.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 64 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  12. 12.What is √1089? =
  13. 13.A square garden has an area of 3249 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 147 must be divided to get a perfect square?
  15. 15.What is the smallest whole number by which 18 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 50² and 51²?
  17. 17.What is √5184? =
  18. 18.What is √6241? =
  19. 19.What is 14²? =
  20. 20.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  23. 23.How many whole numbers lie between 43² and 44²?
  24. 24.A square garden has an area of 1369 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 121 square m. How long is each side (in m)?
  26. 26.What is √3249? =
  27. 27.What is √1369? =
  28. 28.How many whole numbers lie between 32² and 33²?
  29. 29.What is 70²? =
  30. 30.What is 65²? =
  31. 31.What is √2401? =
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 683 (b) 708 (c) 676
  34. 34.A square garden has an area of 169 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 283 (b) 265 (c) 256
  36. 36.What is √3364? =
  37. 37.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  38. 38.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  39. 39.What is √841? =
  40. 40.What is the smallest whole number by which 125 must be divided to get a perfect square?

Answer key

  1. 40
  2. 24
  3. 32
  4. 625
  5. 95
  6. 48
  7. 17
  8. 3
  9. 6
  10. 8
  11. 13
  12. 33
  13. 57
  14. 3
  15. 2
  16. 100
  17. 72
  18. 79
  19. 196
  20. 14
  21. 529
  22. 2
  23. 86
  24. 37
  25. 11
  26. 57
  27. 37
  28. 64
  29. 4900
  30. 4225
  31. 49
  32. 400
  33. 676
  34. 13
  35. 256
  36. 58
  37. 5
  38. 6
  39. 29
  40. 5

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