← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 610 · 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.How many whole numbers lie between 8² and 9²?
  3. 3.What is √3481? =
  4. 4.Which of these is a perfect square? (a) 372 (b) 361 (c) 365
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is 18²? =
  8. 8.What is √196? =
  9. 9.What is √3136? =
  10. 10.How many whole numbers lie between 41² and 42²?
  11. 11.What is the smallest whole number by which 44 must be divided to get a perfect square?
  12. 12.What is √1600? =
  13. 13.What is √6400? =
  14. 14.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  15. 15.What is 77²? =
  16. 16.What is 52²? =
  17. 17.How many whole numbers lie between 35² and 36²?
  18. 18.How many whole numbers lie between 18² and 19²?
  19. 19.Which of these is a perfect square? (a) 517 (b) 484 (c) 513
  20. 20.What is the smallest whole number by which 72 must be divided to get a perfect square?
  21. 21.What is the smallest whole number by which 735 must be divided to get a perfect square?
  22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 28² and 29²?
  24. 24.What is 73²? =
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 289 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 2704 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 128 must be divided to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 439 (b) 400 (c) 412
  30. 30.What is 89²? =
  31. 31.What is √4096? =
  32. 32.What is √576? =
  33. 33.What is √2304? =
  34. 34.A square garden has an area of 3249 square m. How long is each side (in m)?
  35. 35.What is √9216? =
  36. 36.How many whole numbers lie between 14² and 15²?
  37. 37.What is the smallest whole number by which 28 must be divided to get a perfect square?
  38. 38.What is √2209? =
  39. 39.What is √1156? =
  40. 40.What is the smallest whole number by which 343 must be multiplied to get a perfect square?

Answer key

  1. 32
  2. 16
  3. 59
  4. 361
  5. 841
  6. 25
  7. 324
  8. 14
  9. 56
  10. 82
  11. 11
  12. 40
  13. 80
  14. 15
  15. 5929
  16. 2704
  17. 70
  18. 36
  19. 484
  20. 2
  21. 15
  22. 484
  23. 56
  24. 5329
  25. 625
  26. 17
  27. 52
  28. 2
  29. 400
  30. 7921
  31. 64
  32. 24
  33. 48
  34. 57
  35. 96
  36. 28
  37. 7
  38. 47
  39. 34
  40. 7

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