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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 553 · 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 17²? =
  2. 2.What is √2809? =
  3. 3.Which of these is a perfect square? (a) 1408 (b) 1399 (c) 1369
  4. 4.A square garden has an area of 169 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 2304 square m. How long is each side (in m)?
  6. 6.What is 54²? =
  7. 7.What is √9216? =
  8. 8.What is √784? =
  9. 9.How many whole numbers lie between 16² and 17²?
  10. 10.A square garden has an area of 2209 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √4624? =
  13. 13.How many whole numbers lie between 17² and 18²?
  14. 14.What is 79²? =
  15. 15.A square garden has an area of 64 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 107 (b) 105 (c) 100
  17. 17.What is the smallest whole number by which 448 must be divided to get a perfect square?
  18. 18.A square garden has an area of 324 square m. How long is each side (in m)?
  19. 19.Which of these is a perfect square? (a) 187 (b) 169 (c) 189
  20. 20.What is 20²? =
  21. 21.A square garden has an area of 144 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 1067 (b) 1072 (c) 1024
  23. 23.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 400 square m. How long is each side (in m)?
  27. 27.What is √841? =
  28. 28.What is 83²? =
  29. 29.How many whole numbers lie between 43² and 44²?
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √6084? =
  32. 32.What is the smallest whole number by which 28 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 112 must be divided to get a perfect square?
  34. 34.What is the smallest whole number by which 135 must be divided to get a perfect square?
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  37. 37.What is 94²? =
  38. 38.A square garden has an area of 1225 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 98 must be divided to get a perfect square?
  40. 40.What is 31²? =

Answer key

  1. 289
  2. 53
  3. 1369
  4. 13
  5. 48
  6. 2916
  7. 96
  8. 28
  9. 32
  10. 47
  11. 100
  12. 68
  13. 34
  14. 6241
  15. 8
  16. 100
  17. 7
  18. 18
  19. 169
  20. 400
  21. 12
  22. 1024
  23. 10
  24. 144
  25. 5
  26. 20
  27. 29
  28. 6889
  29. 86
  30. 324
  31. 78
  32. 7
  33. 7
  34. 15
  35. 64
  36. 5
  37. 8836
  38. 35
  39. 2
  40. 961

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