← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 354 · 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 √2116? =
  2. 2.Which of these is a perfect square? (a) 379 (b) 380 (c) 361
  3. 3.Which of these is a perfect square? (a) 900 (b) 927 (c) 917
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √6724? =
  6. 6.What is 35²? =
  7. 7.Which of these is a perfect square? (a) 987 (b) 969 (c) 961
  8. 8.How many whole numbers lie between 30² and 31²?
  9. 9.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  10. 10.What is √3481? =
  11. 11.A square garden has an area of 1849 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 87²? =
  15. 15.What is 94²? =
  16. 16.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  17. 17.What is the smallest whole number by which 63 must be divided to get a perfect square?
  18. 18.What is 36²? =
  19. 19.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 1213 (b) 1201 (c) 1156
  21. 21.A square garden has an area of 3025 square m. How long is each side (in m)?
  22. 22.What is √7225? =
  23. 23.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 2401 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 59²? =
  28. 28.Which of these is a perfect square? (a) 1646 (b) 1600 (c) 1650
  29. 29.Which of these is a perfect square? (a) 1444 (b) 1499 (c) 1497
  30. 30.A square garden has an area of 121 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 1565 (b) 1533 (c) 1521
  32. 32.How many whole numbers lie between 24² and 25²?
  33. 33.Which of these is a perfect square? (a) 841 (b) 848 (c) 860
  34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 3136 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 50² and 51²?
  37. 37.How many whole numbers lie between 5² and 6²?
  38. 38.What is 70²? =
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is √169? =

Answer key

  1. 46
  2. 361
  3. 900
  4. 225
  5. 82
  6. 1225
  7. 961
  8. 60
  9. 14
  10. 59
  11. 43
  12. 3
  13. 676
  14. 7569
  15. 8836
  16. 14
  17. 7
  18. 1296
  19. 11
  20. 1156
  21. 55
  22. 85
  23. 6
  24. 49
  25. 49
  26. 64
  27. 3481
  28. 1600
  29. 1444
  30. 11
  31. 1521
  32. 48
  33. 841
  34. 576
  35. 56
  36. 100
  37. 10
  38. 4900
  39. 784
  40. 13

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