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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 329 · 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 sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  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 896 must be multiplied to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 291 (b) 312 (c) 289
  5. 5.A square garden has an area of 225 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 3481 square m. How long is each side (in m)?
  7. 7.How many whole numbers lie between 49² and 50²?
  8. 8.What is 12²? =
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 289 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 25 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 361 (b) 366 (c) 377
  13. 13.What is 87²? =
  14. 14.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 2401 square m. How long is each side (in m)?
  16. 16.What is √1296? =
  17. 17.How many whole numbers lie between 16² and 17²?
  18. 18.Which of these is a perfect square? (a) 781 (b) 755 (c) 729
  19. 19.What is 79²? =
  20. 20.What is √841? =
  21. 21.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √676? =
  24. 24.A square garden has an area of 400 square m. How long is each side (in m)?
  25. 25.What is √9801? =
  26. 26.What is √3025? =
  27. 27.What is 14²? =
  28. 28.What is the smallest whole number by which 32 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 17² and 18²?
  30. 30.What is the smallest whole number by which 162 must be divided to get a perfect square?
  31. 31.A square garden has an area of 961 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 1536 (b) 1521 (c) 1523
  33. 33.What is √1444? =
  34. 34.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 256 (b) 273 (c) 266
  36. 36.Which of these is a perfect square? (a) 704 (b) 676 (c) 690
  37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 50² and 51²?
  39. 39.A square garden has an area of 2500 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 3600 square m. How long is each side (in m)?

Answer key

  1. 225
  2. 81
  3. 14
  4. 289
  5. 15
  6. 59
  7. 98
  8. 144
  9. 144
  10. 17
  11. 5
  12. 361
  13. 7569
  14. 13
  15. 49
  16. 36
  17. 32
  18. 729
  19. 6241
  20. 29
  21. 529
  22. 121
  23. 26
  24. 20
  25. 99
  26. 55
  27. 196
  28. 2
  29. 34
  30. 2
  31. 31
  32. 1521
  33. 38
  34. 10
  35. 256
  36. 676
  37. 36
  38. 100
  39. 50
  40. 60

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