← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 47 · 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 √5625? =
  2. 2.Which of these is a perfect square? (a) 1024 (b) 1033 (c) 1026
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √1024? =
  5. 5.Which of these is a perfect square? (a) 400 (b) 425 (c) 432
  6. 6.What is √3136? =
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.What is the smallest whole number by which 32 must be divided to get a perfect square?
  9. 9.What is the smallest whole number by which 147 must be divided to get a perfect square?
  10. 10.What is the smallest whole number by which 128 must be divided to get a perfect square?
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 121 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 1521 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 310 (b) 294 (c) 289
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 1089 (b) 1140 (c) 1108
  18. 18.Which of these is a perfect square? (a) 909 (b) 900 (c) 916
  19. 19.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 196 square m. How long is each side (in m)?
  21. 21.What is √9216? =
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  24. 24.How many whole numbers lie between 20² and 21²?
  25. 25.What is 84²? =
  26. 26.What is 96²? =
  27. 27.What is 27²? =
  28. 28.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  29. 29.How many whole numbers lie between 25² and 26²?
  30. 30.A square garden has an area of 2209 square m. How long is each side (in m)?
  31. 31.What is 24²? =
  32. 32.What is √2304? =
  33. 33.Which of these is a perfect square? (a) 144 (b) 167 (c) 163
  34. 34.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 35²? =
  36. 36.Which of these is a perfect square? (a) 627 (b) 625 (c) 637
  37. 37.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 1156 square m. How long is each side (in m)?
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 98 must be divided to get a perfect square?

Answer key

  1. 75
  2. 1024
  3. 625
  4. 32
  5. 400
  6. 56
  7. 64
  8. 2
  9. 3
  10. 2
  11. 529
  12. 169
  13. 11
  14. 39
  15. 289
  16. 784
  17. 1089
  18. 900
  19. 10
  20. 14
  21. 96
  22. 36
  23. 2
  24. 40
  25. 7056
  26. 9216
  27. 729
  28. 13
  29. 50
  30. 47
  31. 576
  32. 48
  33. 144
  34. 324
  35. 1225
  36. 625
  37. 2
  38. 34
  39. 144
  40. 2

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