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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 711 · 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 30²? =
  2. 2.Which of these is a perfect square? (a) 683 (b) 676 (c) 695
  3. 3.What is √2500? =
  4. 4.Which of these is a perfect square? (a) 311 (b) 306 (c) 289
  5. 5.What is the smallest whole number by which 147 must be divided to get a perfect square?
  6. 6.A square garden has an area of 81 square m. How long is each side (in m)?
  7. 7.What is 91²? =
  8. 8.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  9. 9.What is 87²? =
  10. 10.What is √5041? =
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 47² and 48²?
  13. 13.How many whole numbers lie between 41² and 42²?
  14. 14.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  15. 15.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  16. 16.What is 52²? =
  17. 17.A square garden has an area of 256 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 37² and 38²?
  19. 19.Which of these is a perfect square? (a) 329 (b) 324 (c) 330
  20. 20.What is √1156? =
  21. 21.What is √400? =
  22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 33²? =
  25. 25.Which of these is a perfect square? (a) 1387 (b) 1369 (c) 1373
  26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √2704? =
  28. 28.What is the smallest whole number by which 72 must be divided to get a perfect square?
  29. 29.What is √7921? =
  30. 30.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  31. 31.What is the smallest whole number by which 108 must be divided to get a perfect square?
  32. 32.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  33. 33.A square garden has an area of 2916 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 112 must be divided to get a perfect square?
  35. 35.A square garden has an area of 1936 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 39² and 40²?
  37. 37.How many whole numbers lie between 34² and 35²?
  38. 38.What is 67²? =
  39. 39.A square garden has an area of 2209 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 900
  2. 676
  3. 50
  4. 289
  5. 3
  6. 9
  7. 8281
  8. 2
  9. 7569
  10. 71
  11. 49
  12. 94
  13. 82
  14. 3
  15. 15
  16. 2704
  17. 16
  18. 74
  19. 324
  20. 34
  21. 20
  22. 81
  23. 841
  24. 1089
  25. 1369
  26. 676
  27. 52
  28. 2
  29. 89
  30. 7
  31. 3
  32. 11
  33. 54
  34. 7
  35. 44
  36. 78
  37. 68
  38. 4489
  39. 47
  40. 729

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