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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 515 · 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 14 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 24² and 25²?
  3. 3.What is √2500? =
  4. 4.How many whole numbers lie between 33² and 34²?
  5. 5.A square garden has an area of 400 square m. How long is each side (in m)?
  6. 6.What is 24²? =
  7. 7.Which of these is a perfect square? (a) 402 (b) 400 (c) 420
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 21²? =
  10. 10.What is 48²? =
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 982 (b) 1000 (c) 961
  13. 13.Which of these is a perfect square? (a) 485 (b) 484 (c) 528
  14. 14.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 1040 (b) 1069 (c) 1024
  16. 16.A square garden has an area of 2500 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 45²? =
  21. 21.A square garden has an area of 3136 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 11² and 12²?
  23. 23.A square garden has an area of 1089 square m. How long is each side (in m)?
  24. 24.What is 12²? =
  25. 25.Which of these is a perfect square? (a) 182 (b) 178 (c) 169
  26. 26.A square garden has an area of 289 square m. How long is each side (in m)?
  27. 27.What is 36²? =
  28. 28.What is √1156? =
  29. 29.What is 18²? =
  30. 30.How many whole numbers lie between 40² and 41²?
  31. 31.How many whole numbers lie between 46² and 47²?
  32. 32.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  34. 34.What is 35²? =
  35. 35.A square garden has an area of 2209 square m. How long is each side (in m)?
  36. 36.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  37. 37.How many whole numbers lie between 20² and 21²?
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 63 must be multiplied to get a perfect square?

Answer key

  1. 196
  2. 48
  3. 50
  4. 66
  5. 20
  6. 576
  7. 400
  8. 169
  9. 441
  10. 2304
  11. 100
  12. 961
  13. 484
  14. 6
  15. 1024
  16. 50
  17. 784
  18. 36
  19. 64
  20. 2025
  21. 56
  22. 22
  23. 33
  24. 144
  25. 169
  26. 17
  27. 1296
  28. 34
  29. 324
  30. 80
  31. 92
  32. 841
  33. 14
  34. 1225
  35. 47
  36. 10
  37. 40
  38. 289
  39. 49
  40. 7

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