← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 210 · 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.A square garden has an area of 1024 square m. How long is each side (in m)?
  2. 2.What is 36²? =
  3. 3.What is 39²? =
  4. 4.A square garden has an area of 225 square m. How long is each side (in m)?
  5. 5.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √1849? =
  7. 7.Which of these is a perfect square? (a) 1600 (b) 1620 (c) 1625
  8. 8.Which of these is a perfect square? (a) 187 (b) 174 (c) 169
  9. 9.A square garden has an area of 529 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 81 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 148 (b) 144 (c) 167
  12. 12.Which of these is a perfect square? (a) 569 (b) 529 (c) 553
  13. 13.How many whole numbers lie between 22² and 23²?
  14. 14.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 150 must be divided to get a perfect square?
  18. 18.What is √625? =
  19. 19.What is √961? =
  20. 20.Which of these is a perfect square? (a) 1462 (b) 1492 (c) 1444
  21. 21.What is √225? =
  22. 22.How many whole numbers lie between 35² and 36²?
  23. 23.What is √3249? =
  24. 24.What is 20²? =
  25. 25.What is √3025? =
  26. 26.How many whole numbers lie between 36² and 37²?
  27. 27.What is the smallest whole number by which 175 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 12² and 13²?
  29. 29.A square garden has an area of 400 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 270 (b) 256 (c) 265
  31. 31.What is √7744? =
  32. 32.What is √4096? =
  33. 33.What is √7569? =
  34. 34.How many whole numbers lie between 33² and 34²?
  35. 35.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  36. 36.How many whole numbers lie between 18² and 19²?
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √6241? =
  39. 39.What is √5625? =
  40. 40.What is the smallest whole number by which 176 must be multiplied to get a perfect square?

Answer key

  1. 32
  2. 1296
  3. 1521
  4. 15
  5. 400
  6. 43
  7. 1600
  8. 169
  9. 23
  10. 9
  11. 144
  12. 529
  13. 44
  14. 11
  15. 36
  16. 529
  17. 6
  18. 25
  19. 31
  20. 1444
  21. 15
  22. 70
  23. 57
  24. 400
  25. 55
  26. 72
  27. 7
  28. 24
  29. 20
  30. 256
  31. 88
  32. 64
  33. 87
  34. 66
  35. 15
  36. 36
  37. 25
  38. 79
  39. 75
  40. 11

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