← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 156 · 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 56 must be multiplied to get a perfect square?
  2. 2.What is √9216? =
  3. 3.What is 14²? =
  4. 4.What is 92²? =
  5. 5.A square garden has an area of 324 square m. How long is each side (in m)?
  6. 6.What is √144? =
  7. 7.What is √2401? =
  8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 529 (b) 548 (c) 554
  10. 10.Which of these is a perfect square? (a) 400 (b) 419 (c) 422
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 25² and 26²?
  15. 15.How many whole numbers lie between 14² and 15²?
  16. 16.How many whole numbers lie between 49² and 50²?
  17. 17.What is 57²? =
  18. 18.What is √9025? =
  19. 19.A square garden has an area of 961 square m. How long is each side (in m)?
  20. 20.What is 28²? =
  21. 21.What is 34²? =
  22. 22.Which of these is a perfect square? (a) 933 (b) 959 (c) 900
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 486 must be divided to get a perfect square?
  26. 26.What is √3364? =
  27. 27.What is 11²? =
  28. 28.What is the smallest whole number by which 540 must be divided to get a perfect square?
  29. 29.What is 42²? =
  30. 30.A square garden has an area of 64 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 1369 (b) 1373 (c) 1417
  32. 32.Which of these is a perfect square? (a) 331 (b) 324 (c) 347
  33. 33.What is 66²? =
  34. 34.How many whole numbers lie between 36² and 37²?
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  37. 37.What is 85²? =
  38. 38.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 28² and 29²?
  40. 40.What is √400? =

Answer key

  1. 14
  2. 96
  3. 196
  4. 8464
  5. 18
  6. 12
  7. 49
  8. 289
  9. 529
  10. 400
  11. 25
  12. 15
  13. 324
  14. 50
  15. 28
  16. 98
  17. 3249
  18. 95
  19. 31
  20. 784
  21. 1156
  22. 900
  23. 841
  24. 64
  25. 6
  26. 58
  27. 121
  28. 15
  29. 1764
  30. 8
  31. 1369
  32. 324
  33. 4356
  34. 72
  35. 100
  36. 3
  37. 7225
  38. 625
  39. 56
  40. 20

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