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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 726 · 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 7² and 8²?
  2. 2.How many whole numbers lie between 26² and 27²?
  3. 3.Which of these is a perfect square? (a) 161 (b) 162 (c) 144
  4. 4.What is the smallest whole number by which 60 must be divided to get a perfect square?
  5. 5.What is the smallest whole number by which 18 must be divided to get a perfect square?
  6. 6.What is √1600? =
  7. 7.What is 67²? =
  8. 8.What is √3721? =
  9. 9.A square garden has an area of 3025 square m. How long is each side (in m)?
  10. 10.What is √4356? =
  11. 11.A square garden has an area of 2304 square m. How long is each side (in m)?
  12. 12.What is 63²? =
  13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 484 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 576 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is 52²? =
  19. 19.How many whole numbers lie between 29² and 30²?
  20. 20.Which of these is a perfect square? (a) 818 (b) 784 (c) 805
  21. 21.What is √1156? =
  22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 95²? =
  24. 24.What is the smallest whole number by which 40 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 436 (b) 420 (c) 400
  26. 26.How many whole numbers lie between 23² and 24²?
  27. 27.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 1047 (b) 1053 (c) 1024
  29. 29.How many whole numbers lie between 13² and 14²?
  30. 30.How many whole numbers lie between 43² and 44²?
  31. 31.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 374 (b) 361 (c) 398
  33. 33.How many whole numbers lie between 17² and 18²?
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √3249? =
  36. 36.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 11² and 12²?
  40. 40.What is √9025? =

Answer key

  1. 14
  2. 52
  3. 144
  4. 15
  5. 2
  6. 40
  7. 4489
  8. 61
  9. 55
  10. 66
  11. 48
  12. 3969
  13. 784
  14. 484
  15. 22
  16. 24
  17. 81
  18. 2704
  19. 58
  20. 784
  21. 34
  22. 225
  23. 9025
  24. 10
  25. 400
  26. 46
  27. 400
  28. 1024
  29. 26
  30. 86
  31. 3
  32. 361
  33. 34
  34. 49
  35. 57
  36. 15
  37. 361
  38. 100
  39. 22
  40. 95

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