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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 724 · 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.How many whole numbers lie between 8² and 9²?
  2. 2.How many whole numbers lie between 44² and 45²?
  3. 3.What is √1521? =
  4. 4.What is 33²? =
  5. 5.What is 51²? =
  6. 6.How many whole numbers lie between 43² and 44²?
  7. 7.What is √4356? =
  8. 8.What is √7396? =
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 98²? =
  11. 11.What is 19²? =
  12. 12.What is √2401? =
  13. 13.How many whole numbers lie between 20² and 21²?
  14. 14.What is 40²? =
  15. 15.A square garden has an area of 2304 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 2601 square m. How long is each side (in m)?
  17. 17.What is 68²? =
  18. 18.How many whole numbers lie between 19² and 20²?
  19. 19.What is the smallest whole number by which 343 must be divided to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 903 (b) 942 (c) 900
  21. 21.A square garden has an area of 36 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 150 must be divided to get a perfect square?
  24. 24.A square garden has an area of 3249 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 144 square m. How long is each side (in m)?
  26. 26.What is 27²? =
  27. 27.What is the smallest whole number by which 243 must be divided to get a perfect square?
  28. 28.What is √3136? =
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 26² and 27²?
  31. 31.What is the smallest whole number by which 126 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 884 (b) 848 (c) 841
  33. 33.What is 42²? =
  34. 34.What is √3600? =
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 77²? =
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 324 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 16² and 17²?

Answer key

  1. 16
  2. 88
  3. 39
  4. 1089
  5. 2601
  6. 86
  7. 66
  8. 86
  9. 784
  10. 9604
  11. 361
  12. 49
  13. 40
  14. 1600
  15. 48
  16. 51
  17. 4624
  18. 38
  19. 7
  20. 900
  21. 6
  22. 7
  23. 6
  24. 57
  25. 12
  26. 729
  27. 3
  28. 56
  29. 64
  30. 52
  31. 14
  32. 841
  33. 1764
  34. 60
  35. 289
  36. 5929
  37. 49
  38. 361
  39. 18
  40. 32

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