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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 465 · 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 the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 564 (b) 529 (c) 548
  3. 3.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 47² and 48²?
  5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  9. 9.What is 12²? =
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  12. 12.What is 48²? =
  13. 13.What is √2704? =
  14. 14.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 841 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 3136 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 48² and 49²?
  19. 19.How many whole numbers lie between 44² and 45²?
  20. 20.A square garden has an area of 1444 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 17² and 18²?
  22. 22.Which of these is a perfect square? (a) 1470 (b) 1444 (c) 1515
  23. 23.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  24. 24.What is 73²? =
  25. 25.How many whole numbers lie between 20² and 21²?
  26. 26.How many whole numbers lie between 36² and 37²?
  27. 27.What is the smallest whole number by which 208 must be divided to get a perfect square?
  28. 28.What is 26²? =
  29. 29.A square garden has an area of 2304 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 2704 square m. How long is each side (in m)?
  31. 31.What is 74²? =
  32. 32.What is √169? =
  33. 33.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 1661 (b) 1675 (c) 1600
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 176 (b) 169 (c) 175
  37. 37.Which of these is a perfect square? (a) 266 (b) 287 (c) 256
  38. 38.What is 34²? =
  39. 39.A square garden has an area of 625 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 961 square m. How long is each side (in m)?

Answer key

  1. 121
  2. 529
  3. 676
  4. 94
  5. 900
  6. 361
  7. 256
  8. 10
  9. 144
  10. 484
  11. 7
  12. 2304
  13. 52
  14. 841
  15. 29
  16. 56
  17. 576
  18. 96
  19. 88
  20. 38
  21. 34
  22. 1444
  23. 7
  24. 5329
  25. 40
  26. 72
  27. 13
  28. 676
  29. 48
  30. 52
  31. 5476
  32. 13
  33. 3
  34. 1600
  35. 49
  36. 169
  37. 256
  38. 1156
  39. 25
  40. 31

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