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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 550 · 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 the smallest whole number by which 99 must be divided to get a perfect square?
  2. 2.How many whole numbers lie between 47² and 48²?
  3. 3.What is √3364? =
  4. 4.Which of these is a perfect square? (a) 961 (b) 995 (c) 970
  5. 5.What is the smallest whole number by which 20 must be divided to get a perfect square?
  6. 6.What is the smallest whole number by which 810 must be divided to get a perfect square?
  7. 7.What is the smallest whole number by which 63 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  9. 9.What is √7225? =
  10. 10.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  11. 11.What is √5476? =
  12. 12.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  13. 13.How many whole numbers lie between 48² and 49²?
  14. 14.Which of these is a perfect square? (a) 480 (b) 477 (c) 441
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the smallest whole number by which 396 must be divided to get a perfect square?
  17. 17.What is √729? =
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  20. 20.What is 12²? =
  21. 21.How many whole numbers lie between 32² and 33²?
  22. 22.What is √5184? =
  23. 23.How many whole numbers lie between 25² and 26²?
  24. 24.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 169 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 44² and 45²?
  27. 27.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  28. 28.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 100 (b) 114 (c) 120
  30. 30.What is 34²? =
  31. 31.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 71²? =
  33. 33.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 325 (b) 324 (c) 356
  37. 37.How many whole numbers lie between 8² and 9²?
  38. 38.What is √841? =
  39. 39.What is √6084? =
  40. 40.What is the smallest whole number by which 162 must be divided to get a perfect square?

Answer key

  1. 11
  2. 94
  3. 58
  4. 961
  5. 5
  6. 10
  7. 7
  8. 14
  9. 85
  10. 13
  11. 74
  12. 2
  13. 96
  14. 441
  15. 196
  16. 11
  17. 27
  18. 676
  19. 3
  20. 144
  21. 64
  22. 72
  23. 50
  24. 900
  25. 13
  26. 88
  27. 2
  28. 13
  29. 100
  30. 1156
  31. 36
  32. 5041
  33. 7
  34. 13
  35. 121
  36. 324
  37. 16
  38. 29
  39. 78
  40. 2

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