Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 727 · 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 17²? =
2. 2.Which of these is a perfect square? (a) 256 (b) 286 (c) 273
3. 3.How many whole numbers lie between 38² and 39²?
4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 57²? =
6. 6.What is 53²? =
7. 7.Which of these is a perfect square? (a) 1108 (b) 1093 (c) 1089
8. 8.What is 92²? =
9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 90²? =
11. 11.A square garden has an area of 2601 square m. How long is each side (in m)?
12. 12.What is 87²? =
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
14. 14.Which of these is a perfect square? (a) 627 (b) 625 (c) 630
15. 15.What is 23²? =
16. 16.What is 31²? =
17. 17.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
18. 18.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
20. 20.What is 36²? =
21. 21.What is the smallest whole number by which 240 must be divided to get a perfect square?
22. 22.What is √256? =
23. 23.What is the smallest whole number by which 567 must be divided to get a perfect square?
24. 24.How many whole numbers lie between 18² and 19²?
25. 25.A square garden has an area of 196 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
28. 28.A square garden has an area of 3364 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 798 (b) 823 (c) 784
30. 30.How many whole numbers lie between 26² and 27²?
31. 31.What is 66²? =
32. 32.What is √4489? =
33. 33.Which of these is a perfect square? (a) 441 (b) 471 (c) 445
34. 34.A square garden has an area of 3025 square m. How long is each side (in m)?
35. 35.What is √7921? =
36. 36.A square garden has an area of 441 square m. How long is each side (in m)?
37. 37.What is 37²? =
38. 38.How many whole numbers lie between 50² and 51²?
39. 39.A square garden has an area of 400 square m. How long is each side (in m)?
40. 40.What is √576? =

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