Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 289 · 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.Which of these is a perfect square? (a) 676 (b) 715 (c) 695
2. 2.What is 56²? =
3. 3.A square garden has an area of 2500 square m. How long is each side (in m)?
4. 4.What is 21²? =
5. 5.How many whole numbers lie between 46² and 47²?
6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 17²? =
8. 8.What is 24²? =
9. 9.What is 86²? =
10. 10.A square garden has an area of 484 square m. How long is each side (in m)?
11. 11.A square garden has an area of 3600 square m. How long is each side (in m)?
12. 12.What is 34²? =
13. 13.How many whole numbers lie between 10² and 11²?
14. 14.What is 65²? =
15. 15.A square garden has an area of 841 square m. How long is each side (in m)?
16. 16.Which of these is a perfect square? (a) 854 (b) 843 (c) 841
17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √289? =
19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
21. 21.What is √5184? =
22. 22.What is √576? =
23. 23.A square garden has an area of 2916 square m. How long is each side (in m)?
24. 24.What is √2116? =
25. 25.Which of these is a perfect square? (a) 440 (b) 403 (c) 400
26. 26.What is 44²? =
27. 27.What is the smallest whole number by which 147 must be divided to get a perfect square?
28. 28.What is √1521? =
29. 29.What is 42²? =
30. 30.What is the smallest whole number by which 245 must be divided to get a perfect square?
31. 31.Which of these is a perfect square? (a) 1112 (b) 1147 (c) 1089
32. 32.What is the smallest whole number by which 80 must be divided to get a perfect square?
33. 33.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
34. 34.Which of these is a perfect square? (a) 742 (b) 729 (c) 773
35. 35.What is 48²? =
36. 36.A square garden has an area of 1521 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
38. 38.What is 46²? =
39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
40. 40.How many whole numbers lie between 28² and 29²?

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