← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 101 · 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 √5329? =
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 25 square m. How long is each side (in m)?
  4. 4.What is √324? =
  5. 5.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 1234 (b) 1270 (c) 1225
  7. 7.What is √5184? =
  8. 8.A square garden has an area of 64 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 31² and 32²?
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √1225? =
  12. 12.Which of these is a perfect square? (a) 367 (b) 363 (c) 361
  13. 13.What is 82²? =
  14. 14.What is 40²? =
  15. 15.What is √9025? =
  16. 16.Which of these is a perfect square? (a) 256 (b) 267 (c) 282
  17. 17.What is 87²? =
  18. 18.What is √576? =
  19. 19.What is √6084? =
  20. 20.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 113 (b) 100 (c) 117
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 37²? =
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √400? =
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 19²? =
  28. 28.How many whole numbers lie between 9² and 10²?
  29. 29.How many whole numbers lie between 48² and 49²?
  30. 30.What is √3364? =
  31. 31.Which of these is a perfect square? (a) 1618 (b) 1601 (c) 1600
  32. 32.How many whole numbers lie between 17² and 18²?
  33. 33.Which of these is a perfect square? (a) 702 (b) 691 (c) 676
  34. 34.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  35. 35.What is √225? =
  36. 36.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 735 must be divided to get a perfect square?
  38. 38.A square garden has an area of 144 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 478 (b) 461 (c) 441
  40. 40.How many whole numbers lie between 18² and 19²?

Answer key

  1. 73
  2. 841
  3. 5
  4. 18
  5. 7
  6. 1225
  7. 72
  8. 8
  9. 62
  10. 441
  11. 35
  12. 361
  13. 6724
  14. 1600
  15. 95
  16. 256
  17. 7569
  18. 24
  19. 78
  20. 13
  21. 100
  22. 400
  23. 1369
  24. 36
  25. 20
  26. 49
  27. 361
  28. 18
  29. 96
  30. 58
  31. 1600
  32. 34
  33. 676
  34. 2
  35. 15
  36. 324
  37. 15
  38. 12
  39. 441
  40. 36

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets