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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 319 · 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 smallest whole number by which 810 must be multiplied to get a perfect square?
  2. 2.What is 70²? =
  3. 3.What is the smallest whole number by which 896 must be divided to get a perfect square?
  4. 4.What is √9025? =
  5. 5.A square garden has an area of 3025 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 1369 (b) 1378 (c) 1436
  7. 7.Which of these is a perfect square? (a) 364 (b) 361 (c) 399
  8. 8.What is √4761? =
  9. 9.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 1450 (b) 1490 (c) 1444
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  13. 13.What is 45²? =
  14. 14.Which of these is a perfect square? (a) 172 (b) 169 (c) 194
  15. 15.A square garden has an area of 676 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √4489? =
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 62²? =
  20. 20.What is 40²? =
  21. 21.How many whole numbers lie between 9² and 10²?
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √1600? =
  24. 24.What is 32²? =
  25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  27. 27.What is √3136? =
  28. 28.How many whole numbers lie between 36² and 37²?
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √1849? =
  31. 31.What is 95²? =
  32. 32.What is √3249? =
  33. 33.Which of these is a perfect square? (a) 139 (b) 123 (c) 121
  34. 34.What is 94²? =
  35. 35.What is √3600? =
  36. 36.What is 92²? =
  37. 37.A square garden has an area of 1521 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 2025 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
  40. 40.What is √6084? =

Answer key

  1. 10
  2. 4900
  3. 14
  4. 95
  5. 55
  6. 1369
  7. 361
  8. 69
  9. 5
  10. 1444
  11. 144
  12. 14
  13. 2025
  14. 169
  15. 26
  16. 441
  17. 67
  18. 81
  19. 3844
  20. 1600
  21. 18
  22. 25
  23. 40
  24. 1024
  25. 64
  26. 2
  27. 56
  28. 72
  29. 196
  30. 43
  31. 9025
  32. 57
  33. 121
  34. 8836
  35. 60
  36. 8464
  37. 39
  38. 45
  39. 42
  40. 78

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