← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 334 · 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 400 square m. How long is each side (in m)?
  2. 2.How many whole numbers lie between 18² and 19²?
  3. 3.A square garden has an area of 625 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 24² and 25²?
  5. 5.Which of these is a perfect square? (a) 116 (b) 100 (c) 107
  6. 6.What is 75²? =
  7. 7.Which of these is a perfect square? (a) 1051 (b) 1024 (c) 1082
  8. 8.A square garden has an area of 676 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 75 must be divided to get a perfect square?
  10. 10.A square garden has an area of 1849 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 8² and 9²?
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 50² and 51²?
  14. 14.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  15. 15.What is √1600? =
  16. 16.Which of these is a perfect square? (a) 196 (b) 220 (c) 218
  17. 17.A square garden has an area of 2209 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 1251 (b) 1246 (c) 1225
  19. 19.How many whole numbers lie between 5² and 6²?
  20. 20.Which of these is a perfect square? (a) 289 (b) 304 (c) 313
  21. 21.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  22. 22.What is 92²? =
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √1156? =
  25. 25.Which of these is a perfect square? (a) 1179 (b) 1223 (c) 1156
  26. 26.What is 24²? =
  27. 27.What is 12²? =
  28. 28.A square garden has an area of 196 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 37² and 38²?
  30. 30.Which of these is a perfect square? (a) 961 (b) 981 (c) 997
  31. 31.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  32. 32.What is √2025? =
  33. 33.How many whole numbers lie between 6² and 7²?
  34. 34.Which of these is a perfect square? (a) 1622 (b) 1675 (c) 1600
  35. 35.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  36. 36.How many whole numbers lie between 23² and 24²?
  37. 37.What is the smallest whole number by which 20 must be divided to get a perfect square?
  38. 38.A square garden has an area of 289 square m. How long is each side (in m)?
  39. 39.What is √9409? =
  40. 40.What is √2704? =

Answer key

  1. 20
  2. 36
  3. 25
  4. 48
  5. 100
  6. 5625
  7. 1024
  8. 26
  9. 3
  10. 43
  11. 16
  12. 196
  13. 100
  14. 3
  15. 40
  16. 196
  17. 47
  18. 1225
  19. 10
  20. 289
  21. 7
  22. 8464
  23. 121
  24. 34
  25. 1156
  26. 576
  27. 144
  28. 14
  29. 74
  30. 961
  31. 6
  32. 45
  33. 12
  34. 1600
  35. 7
  36. 46
  37. 5
  38. 17
  39. 97
  40. 52

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