← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 30 · 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 √400? =
  2. 2.How many whole numbers lie between 34² and 35²?
  3. 3.Which of these is a perfect square? (a) 526 (b) 484 (c) 508
  4. 4.Which of these is a perfect square? (a) 576 (b) 614 (c) 615
  5. 5.A square garden has an area of 841 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 49 square m. How long is each side (in m)?
  7. 7.How many whole numbers lie between 9² and 10²?
  8. 8.What is 40²? =
  9. 9.What is the smallest whole number by which 45 must be divided to get a perfect square?
  10. 10.What is 69²? =
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 729 square m. How long is each side (in m)?
  13. 13.What is 23²? =
  14. 14.Which of these is a perfect square? (a) 1301 (b) 1296 (c) 1302
  15. 15.Which of these is a perfect square? (a) 107 (b) 100 (c) 119
  16. 16.How many whole numbers lie between 21² and 22²?
  17. 17.A square garden has an area of 1225 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 11² and 12²?
  19. 19.Which of these is a perfect square? (a) 784 (b) 827 (c) 785
  20. 20.What is 45²? =
  21. 21.Which of these is a perfect square? (a) 167 (b) 145 (c) 144
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 16² and 17²?
  24. 24.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  25. 25.A square garden has an area of 2601 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the smallest whole number by which 245 must be divided to get a perfect square?
  28. 28.What is 96²? =
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  30. 30.Which of these is a perfect square? (a) 174 (b) 190 (c) 169
  31. 31.What is the smallest whole number by which 252 must be divided to get a perfect square?
  32. 32.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  33. 33.What is √1156? =
  34. 34.What is 37²? =
  35. 35.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 2500 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  39. 39.A square garden has an area of 100 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 5² and 6²?

Answer key

  1. 20
  2. 68
  3. 484
  4. 576
  5. 29
  6. 7
  7. 18
  8. 1600
  9. 5
  10. 4761
  11. 256
  12. 27
  13. 529
  14. 1296
  15. 100
  16. 42
  17. 35
  18. 22
  19. 784
  20. 2025
  21. 144
  22. 900
  23. 32
  24. 6
  25. 51
  26. 81
  27. 5
  28. 9216
  29. 529
  30. 169
  31. 7
  32. 15
  33. 34
  34. 1369
  35. 14
  36. 2
  37. 50
  38. 7
  39. 10
  40. 10

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