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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 232 · 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 sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 289 square m. How long is each side (in m)?
  4. 4.What is √576? =
  5. 5.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 168 (b) 161 (c) 144
  7. 7.A square garden has an area of 3249 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  9. 9.What is 42²? =
  10. 10.What is √7225? =
  11. 11.What is the smallest whole number by which 150 must be divided to get a perfect square?
  12. 12.How many whole numbers lie between 39² and 40²?
  13. 13.What is 87²? =
  14. 14.What is 64²? =
  15. 15.What is 17²? =
  16. 16.Which of these is a perfect square? (a) 424 (b) 418 (c) 400
  17. 17.What is √3364? =
  18. 18.How many whole numbers lie between 19² and 20²?
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 98²? =
  21. 21.How many whole numbers lie between 10² and 11²?
  22. 22.A square garden has an area of 900 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 32² and 33²?
  24. 24.Which of these is a perfect square? (a) 1439 (b) 1369 (c) 1386
  25. 25.What is 48²? =
  26. 26.What is the smallest whole number by which 99 must be divided to get a perfect square?
  27. 27.A square garden has an area of 784 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 18² and 19²?
  29. 29.What is the smallest whole number by which 96 must be divided to get a perfect square?
  30. 30.What is √4900? =
  31. 31.Which of these is a perfect square? (a) 964 (b) 994 (c) 961
  32. 32.How many whole numbers lie between 8² and 9²?
  33. 33.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 176 (b) 182 (c) 169
  35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 453 (b) 477 (c) 441
  37. 37.How many whole numbers lie between 30² and 31²?
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 484 (b) 513 (c) 496
  40. 40.A square garden has an area of 324 square m. How long is each side (in m)?

Answer key

  1. 900
  2. 7
  3. 17
  4. 24
  5. 2
  6. 144
  7. 57
  8. 3
  9. 1764
  10. 85
  11. 6
  12. 78
  13. 7569
  14. 4096
  15. 289
  16. 400
  17. 58
  18. 38
  19. 81
  20. 9604
  21. 20
  22. 30
  23. 64
  24. 1369
  25. 2304
  26. 11
  27. 28
  28. 36
  29. 6
  30. 70
  31. 961
  32. 16
  33. 7
  34. 169
  35. 576
  36. 441
  37. 60
  38. 441
  39. 484
  40. 18

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