Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 449 · 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 √8836? =
2. 2.What is √676? =
3. 3.What is √144? =
4. 4.How many whole numbers lie between 10² and 11²?
5. 5.Which of these is a perfect square? (a) 169 (b) 192 (c) 172
6. 6.Which of these is a perfect square? (a) 1537 (b) 1567 (c) 1521
7. 7.Which of these is a perfect square? (a) 784 (b) 836 (c) 829
8. 8.Which of these is a perfect square? (a) 841 (b) 865 (c) 889
9. 9.What is 44²? =
10. 10.What is the smallest whole number by which 567 must be divided to get a perfect square?
11. 11.What is 13²? =
12. 12.What is √961? =
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 25²? =
15. 15.How many whole numbers lie between 12² and 13²?
16. 16.What is 63²? =
17. 17.What is 85²? =
18. 18.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
21. 21.A square garden has an area of 2116 square m. How long is each side (in m)?
22. 22.What is 33²? =
23. 23.Which of these is a perfect square? (a) 324 (b) 331 (c) 329
24. 24.What is 29²? =
25. 25.What is 87²? =
26. 26.What is 66²? =
27. 27.What is √8464? =
28. 28.How many whole numbers lie between 25² and 26²?
29. 29.Which of these is a perfect square? (a) 711 (b) 721 (c) 676
30. 30.Which of these is a perfect square? (a) 542 (b) 529 (c) 531
31. 31.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 832 must be divided to get a perfect square?
33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
34. 34.What is 84²? =
35. 35.Which of these is a perfect square? (a) 127 (b) 121 (c) 136
36. 36.A square garden has an area of 729 square m. How long is each side (in m)?
37. 37.A square garden has an area of 1444 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 8² and 9²?
39. 39.What is 58²? =
40. 40.Which of these is a perfect square? (a) 900 (b) 929 (c) 911

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