Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 1 · 40 sums

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.

1. 1.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
3. 3.What is 64²? =
4. 4.What is 46²? =
5. 5.Which of these is a perfect square? (a) 127 (b) 121 (c) 124
6. 6.What is √900? =
7. 7.What is √5929? =
8. 8.How many whole numbers lie between 6² and 7²?
9. 9.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
10. 10.Which of these is a perfect square? (a) 682 (b) 688 (c) 676
11. 11.What is the smallest whole number by which 735 must be divided to get a perfect square?
12. 12.What is the smallest whole number by which 832 must be divided to get a perfect square?
13. 13.A square garden has an area of 49 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 285 (b) 269 (c) 256
15. 15.What is 22²? =
16. 16.What is 51²? =
17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 12² and 13²?
19. 19.How many whole numbers lie between 20² and 21²?
20. 20.How many whole numbers lie between 43² and 44²?
21. 21.What is 24²? =
22. 22.What is the smallest whole number by which 1134 must be divided to get a perfect square?
23. 23.What is √4225? =
24. 24.How many whole numbers lie between 34² and 35²?
25. 25.A square garden has an area of 121 square m. How long is each side (in m)?
26. 26.A square garden has an area of 625 square m. How long is each side (in m)?
27. 27.How many whole numbers lie between 28² and 29²?
28. 28.A square garden has an area of 900 square m. How long is each side (in m)?
29. 29.What is √529? =
30. 30.What is √576? =
31. 31.How many whole numbers lie between 25² and 26²?
32. 32.A square garden has an area of 1296 square m. How long is each side (in m)?
33. 33.What is 11²? =
34. 34.What is √8100? =
35. 35.What is √5476? =
36. 36.A square garden has an area of 576 square m. How long is each side (in m)?
37. 37.How many whole numbers lie between 42² and 43²?
38. 38.What is 32²? =
39. 39.How many whole numbers lie between 26² and 27²?
40. 40.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?

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