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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 712 · 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.A square garden has an area of 49 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 73²? =
  5. 5.Which of these is a perfect square? (a) 117 (b) 100 (c) 119
  6. 6.What is the smallest whole number by which 32 must be divided to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 305 (b) 303 (c) 289
  8. 8.Which of these is a perfect square? (a) 282 (b) 275 (c) 256
  9. 9.Which of these is a perfect square? (a) 162 (b) 145 (c) 144
  10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 144 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 256 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  15. 15.What is √9216? =
  16. 16.Which of these is a perfect square? (a) 676 (b) 680 (c) 716
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is 32²? =
  19. 19.A square garden has an area of 25 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 625 (b) 641 (c) 631
  21. 21.What is √121? =
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 35²? =
  24. 24.What is 25²? =
  25. 25.A square garden has an area of 2601 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1555 (b) 1579 (c) 1521
  27. 27.What is √7056? =
  28. 28.Which of these is a perfect square? (a) 225 (b) 244 (c) 243
  29. 29.What is the smallest whole number by which 27 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 31² and 32²?
  31. 31.A square garden has an area of 441 square m. How long is each side (in m)?
  32. 32.What is √7225? =
  33. 33.What is √9801? =
  34. 34.A square garden has an area of 784 square m. How long is each side (in m)?
  35. 35.What is √2401? =
  36. 36.Which of these is a perfect square? (a) 869 (b) 841 (c) 875
  37. 37.What is the smallest whole number by which 108 must be divided to get a perfect square?
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 3481 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 176 must be multiplied to get a perfect square?

Answer key

  1. 7
  2. 6
  3. 225
  4. 5329
  5. 100
  6. 2
  7. 289
  8. 256
  9. 144
  10. 841
  11. 11
  12. 12
  13. 16
  14. 3
  15. 96
  16. 676
  17. 64
  18. 1024
  19. 5
  20. 625
  21. 11
  22. 529
  23. 1225
  24. 625
  25. 51
  26. 1521
  27. 84
  28. 225
  29. 3
  30. 62
  31. 21
  32. 85
  33. 99
  34. 28
  35. 49
  36. 841
  37. 3
  38. 144
  39. 59
  40. 11

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