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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 632 · 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.Which of these is a perfect square? (a) 289 (b) 310 (c) 298
  2. 2.Which of these is a perfect square? (a) 364 (b) 366 (c) 361
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 225 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 1156 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 50² and 51²?
  8. 8.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  10. 10.What is √961? =
  11. 11.A square garden has an area of 324 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  13. 13.What is the smallest whole number by which 99 must be divided to get a perfect square?
  14. 14.How many whole numbers lie between 48² and 49²?
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 664 (b) 630 (c) 625
  17. 17.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  18. 18.What is 34²? =
  19. 19.A square garden has an area of 1369 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  21. 21.How many whole numbers lie between 12² and 13²?
  22. 22.What is √2704? =
  23. 23.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  24. 24.What is √169? =
  25. 25.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 36 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 243 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 7² and 8²?
  29. 29.What is 91²? =
  30. 30.How many whole numbers lie between 25² and 26²?
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 913 (b) 900 (c) 916
  33. 33.How many whole numbers lie between 33² and 34²?
  34. 34.How many whole numbers lie between 17² and 18²?
  35. 35.How many whole numbers lie between 27² and 28²?
  36. 36.Which of these is a perfect square? (a) 111 (b) 110 (c) 100
  37. 37.A square garden has an area of 900 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 16² and 17²?
  39. 39.What is the smallest whole number by which 240 must be divided to get a perfect square?
  40. 40.What is the smallest whole number by which 112 must be multiplied to get a perfect square?

Answer key

  1. 289
  2. 361
  3. 25
  4. 15
  5. 34
  6. 441
  7. 100
  8. 7
  9. 11
  10. 31
  11. 18
  12. 5
  13. 11
  14. 96
  15. 324
  16. 625
  17. 3
  18. 1156
  19. 37
  20. 121
  21. 24
  22. 52
  23. 3
  24. 13
  25. 3
  26. 6
  27. 3
  28. 14
  29. 8281
  30. 50
  31. 64
  32. 900
  33. 66
  34. 34
  35. 54
  36. 100
  37. 30
  38. 32
  39. 15
  40. 7

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