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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 665 · 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 18²? =
  2. 2.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 1284 (b) 1260 (c) 1225
  4. 4.What is √2304? =
  5. 5.What is √2704? =
  6. 6.How many whole numbers lie between 8² and 9²?
  7. 7.A square garden has an area of 1600 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 1063 (b) 1036 (c) 1024
  9. 9.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 361 square m. How long is each side (in m)?
  11. 11.What is 34²? =
  12. 12.What is √1225? =
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 784 (b) 798 (c) 804
  15. 15.What is the smallest whole number by which 80 must be divided to get a perfect square?
  16. 16.What is 51²? =
  17. 17.Which of these is a perfect square? (a) 1600 (b) 1661 (c) 1626
  18. 18.What is the smallest whole number by which 396 must be divided to get a perfect square?
  19. 19.What is 14²? =
  20. 20.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 634 (b) 625 (c) 666
  22. 22.A square garden has an area of 2304 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 113 (b) 100 (c) 111
  24. 24.What is 55²? =
  25. 25.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 256 square m. How long is each side (in m)?
  27. 27.What is 15²? =
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 19² and 20²?
  31. 31.What is 70²? =
  32. 32.What is the smallest whole number by which 252 must be divided to get a perfect square?
  33. 33.A square garden has an area of 2401 square m. How long is each side (in m)?
  34. 34.A square garden has an area of 196 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 448 must be divided to get a perfect square?
  37. 37.What is 85²? =
  38. 38.How many whole numbers lie between 33² and 34²?
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 35² and 36²?

Answer key

  1. 324
  2. 15
  3. 1225
  4. 48
  5. 52
  6. 16
  7. 40
  8. 1024
  9. 15
  10. 19
  11. 1156
  12. 35
  13. 400
  14. 784
  15. 5
  16. 2601
  17. 1600
  18. 11
  19. 196
  20. 7
  21. 625
  22. 48
  23. 100
  24. 3025
  25. 900
  26. 16
  27. 225
  28. 64
  29. 361
  30. 38
  31. 4900
  32. 7
  33. 49
  34. 14
  35. 225
  36. 7
  37. 7225
  38. 66
  39. 441
  40. 70

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