← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 33 · 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 1134 must be multiplied to get a perfect square?
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  4. 4.What is √1764? =
  5. 5.What is √484? =
  6. 6.Which of these is a perfect square? (a) 382 (b) 392 (c) 361
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 24² and 25²?
  10. 10.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  11. 11.What is √400? =
  12. 12.A square garden has an area of 100 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 176 must be divided to get a perfect square?
  14. 14.What is 97²? =
  15. 15.What is the smallest whole number by which 112 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  17. 17.What is the smallest whole number by which 135 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  19. 19.What is √2601? =
  20. 20.What is the smallest whole number by which 125 must be divided to get a perfect square?
  21. 21.What is √1936? =
  22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 175 must be divided to get a perfect square?
  24. 24.What is √441? =
  25. 25.What is 45²? =
  26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 130 (b) 121 (c) 124
  28. 28.What is √361? =
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  30. 30.Which of these is a perfect square? (a) 1237 (b) 1225 (c) 1239
  31. 31.A square garden has an area of 1156 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 45² and 46²?
  33. 33.A square garden has an area of 3025 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 32 must be divided to get a perfect square?
  35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 625 (b) 634 (c) 628
  37. 37.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 11² and 12²?
  39. 39.What is 21²? =
  40. 40.How many whole numbers lie between 33² and 34²?

Answer key

  1. 14
  2. 81
  3. 2
  4. 42
  5. 22
  6. 361
  7. 400
  8. 625
  9. 48
  10. 5
  11. 20
  12. 10
  13. 11
  14. 9409
  15. 7
  16. 2
  17. 15
  18. 6
  19. 51
  20. 5
  21. 44
  22. 484
  23. 7
  24. 21
  25. 2025
  26. 441
  27. 121
  28. 19
  29. 121
  30. 1225
  31. 34
  32. 90
  33. 55
  34. 2
  35. 256
  36. 625
  37. 10
  38. 22
  39. 441
  40. 66

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