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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 674 · 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 784 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 1591 (b) 1521 (c) 1570
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √8100? =
  7. 7.Which of these is a perfect square? (a) 450 (b) 478 (c) 441
  8. 8.What is √4225? =
  9. 9.How many whole numbers lie between 39² and 40²?
  10. 10.What is √1444? =
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 81 square m. How long is each side (in m)?
  13. 13.What is √289? =
  14. 14.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 13² and 14²?
  17. 17.How many whole numbers lie between 11² and 12²?
  18. 18.Which of these is a perfect square? (a) 1185 (b) 1156 (c) 1191
  19. 19.How many whole numbers lie between 44² and 45²?
  20. 20.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 64 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 100 (b) 113 (c) 107
  23. 23.A square garden has an area of 169 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 25²? =
  26. 26.A square garden has an area of 2500 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 20²? =
  29. 29.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  30. 30.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 676 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 2704 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 2209 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 36² and 37²?
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √5476? =
  39. 39.What is √1156? =
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 28
  2. 841
  3. 1521
  4. 441
  5. 676
  6. 90
  7. 441
  8. 65
  9. 78
  10. 38
  11. 144
  12. 9
  13. 17
  14. 6
  15. 64
  16. 26
  17. 22
  18. 1156
  19. 88
  20. 7
  21. 8
  22. 100
  23. 13
  24. 400
  25. 625
  26. 50
  27. 256
  28. 400
  29. 2
  30. 13
  31. 49
  32. 26
  33. 100
  34. 52
  35. 47
  36. 72
  37. 121
  38. 74
  39. 34
  40. 729

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