← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 442 · 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.Which of these is a perfect square? (a) 673 (b) 625 (c) 651
  2. 2.What is 87²? =
  3. 3.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 100 (b) 116 (c) 113
  5. 5.What is √2809? =
  6. 6.How many whole numbers lie between 22² and 23²?
  7. 7.What is √4489? =
  8. 8.What is √576? =
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 19² and 20²?
  11. 11.A square garden has an area of 2916 square m. How long is each side (in m)?
  12. 12.What is √4761? =
  13. 13.Which of these is a perfect square? (a) 720 (b) 676 (c) 678
  14. 14.A square garden has an area of 3136 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 20 must be divided to get a perfect square?
  16. 16.A square garden has an area of 441 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 1389 (b) 1369 (c) 1378
  18. 18.What is 19²? =
  19. 19.How many whole numbers lie between 32² and 33²?
  20. 20.What is 14²? =
  21. 21.What is √1225? =
  22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 59²? =
  24. 24.What is 28²? =
  25. 25.What is √9025? =
  26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 169 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 33² and 34²?
  29. 29.What is 13²? =
  30. 30.How many whole numbers lie between 5² and 6²?
  31. 31.A square garden has an area of 900 square m. How long is each side (in m)?
  32. 32.What is √7921? =
  33. 33.How many whole numbers lie between 18² and 19²?
  34. 34.Which of these is a perfect square? (a) 744 (b) 729 (c) 761
  35. 35.How many whole numbers lie between 41² and 42²?
  36. 36.What is √2704? =
  37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √2025? =
  39. 39.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 396 must be divided to get a perfect square?

Answer key

  1. 625
  2. 7569
  3. 14
  4. 100
  5. 53
  6. 44
  7. 67
  8. 24
  9. 784
  10. 38
  11. 54
  12. 69
  13. 676
  14. 56
  15. 5
  16. 21
  17. 1369
  18. 361
  19. 64
  20. 196
  21. 35
  22. 441
  23. 3481
  24. 784
  25. 95
  26. 400
  27. 13
  28. 66
  29. 169
  30. 10
  31. 30
  32. 89
  33. 36
  34. 729
  35. 82
  36. 52
  37. 529
  38. 45
  39. 3
  40. 11

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