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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 296 · 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 48 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 289 (b) 321 (c) 302
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √6724? =
  6. 6.What is √961? =
  7. 7.What is √9604? =
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √441? =
  10. 10.What is the smallest whole number by which 72 must be divided to get a perfect square?
  11. 11.A square garden has an area of 256 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 361 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 236 (b) 230 (c) 225
  14. 14.What is √2304? =
  15. 15.What is 41²? =
  16. 16.What is the smallest whole number by which 343 must be divided to get a perfect square?
  17. 17.What is √2116? =
  18. 18.Which of these is a perfect square? (a) 555 (b) 567 (c) 529
  19. 19.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 42² and 43²?
  21. 21.What is √2704? =
  22. 22.How many whole numbers lie between 19² and 20²?
  23. 23.What is √1521? =
  24. 24.What is √5625? =
  25. 25.What is the smallest whole number by which 960 must be divided 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.Which of these is a perfect square? (a) 361 (b) 377 (c) 387
  28. 28.What is 47²? =
  29. 29.What is the smallest whole number by which 240 must be divided to get a perfect square?
  30. 30.What is 85²? =
  31. 31.What is 34²? =
  32. 32.What is √1369? =
  33. 33.A square garden has an area of 169 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 43² and 44²?
  37. 37.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 41² and 42²?
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is √625? =

Answer key

  1. 3
  2. 7
  3. 289
  4. 25
  5. 82
  6. 31
  7. 98
  8. 196
  9. 21
  10. 2
  11. 16
  12. 19
  13. 225
  14. 48
  15. 1681
  16. 7
  17. 46
  18. 529
  19. 2
  20. 84
  21. 52
  22. 38
  23. 39
  24. 75
  25. 15
  26. 20
  27. 361
  28. 2209
  29. 15
  30. 7225
  31. 1156
  32. 37
  33. 13
  34. 225
  35. 169
  36. 86
  37. 7
  38. 82
  39. 784
  40. 25

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