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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 304 · 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 √1225? =
  2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 400 (b) 408 (c) 426
  5. 5.A square garden has an area of 2401 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 3136 square m. How long is each side (in m)?
  7. 7.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 114 (b) 100 (c) 111
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 18 must be divided to get a perfect square?
  11. 11.A square garden has an area of 3025 square m. How long is each side (in m)?
  12. 12.What is √6889? =
  13. 13.Which of these is a perfect square? (a) 625 (b) 647 (c) 649
  14. 14.Which of these is a perfect square? (a) 909 (b) 900 (c) 956
  15. 15.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 529 (b) 573 (c) 565
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √144? =
  19. 19.What is the smallest whole number by which 28 must be divided to get a perfect square?
  20. 20.What is 59²? =
  21. 21.A square garden has an area of 64 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 37²? =
  25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 704 must be divided to get a perfect square?
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 57²? =
  29. 29.How many whole numbers lie between 28² and 29²?
  30. 30.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  31. 31.What is the smallest whole number by which 147 must be divided to get a perfect square?
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is the smallest whole number by which 891 must be divided to get a perfect square?
  34. 34.How many whole numbers lie between 24² and 25²?
  35. 35.What is 73²? =
  36. 36.A square garden has an area of 625 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 784 square m. How long is each side (in m)?
  39. 39.What is 86²? =
  40. 40.A square garden has an area of 2809 square m. How long is each side (in m)?

Answer key

  1. 35
  2. 729
  3. 2
  4. 400
  5. 49
  6. 56
  7. 784
  8. 100
  9. 64
  10. 2
  11. 55
  12. 83
  13. 625
  14. 900
  15. 3
  16. 529
  17. 289
  18. 12
  19. 7
  20. 3481
  21. 8
  22. 36
  23. 841
  24. 1369
  25. 144
  26. 11
  27. 900
  28. 3249
  29. 56
  30. 14
  31. 3
  32. 529
  33. 11
  34. 48
  35. 5329
  36. 25
  37. 6
  38. 28
  39. 7396
  40. 53

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