Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 220 · 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 79²? =
2. 2.Which of these is a perfect square? (a) 400 (b) 424 (c) 415
3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
5. 5.A square garden has an area of 1600 square m. How long is each side (in m)?
6. 6.What is 55²? =
7. 7.A square garden has an area of 576 square m. How long is each side (in m)?
8. 8.How many whole numbers lie between 50² and 51²?
9. 9.What is √3844? =
10. 10.A square garden has an area of 2304 square m. How long is each side (in m)?
11. 11.What is √256? =
12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 495 (b) 509 (c) 484
14. 14.What is the smallest whole number by which 384 must be divided to get a perfect square?
15. 15.What is √3481? =
16. 16.What is √576? =
17. 17.What is the smallest whole number by which 128 must be divided to get a perfect square?
18. 18.Which of these is a perfect square? (a) 736 (b) 729 (c) 749
19. 19.Which of these is a perfect square? (a) 566 (b) 543 (c) 529
20. 20.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
21. 21.A square garden has an area of 144 square m. How long is each side (in m)?
22. 22.What is 71²? =
23. 23.Which of these is a perfect square? (a) 1129 (b) 1151 (c) 1089
24. 24.A square garden has an area of 256 square m. How long is each side (in m)?
25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 28²? =
27. 27.What is the smallest whole number by which 8 must be divided to get a perfect square?
28. 28.What is the smallest whole number by which 108 must be divided to get a perfect square?
29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 873 (b) 841 (c) 867
31. 31.What is 16²? =
32. 32.What is 89²? =
33. 33.What is √900? =
34. 34.What is 48²? =
35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the smallest whole number by which 350 must be divided to get a perfect square?
37. 37.How many whole numbers lie between 13² and 14²?
38. 38.What is √9409? =
39. 39.Which of these is a perfect square? (a) 256 (b) 263 (c) 259
40. 40.What is √729? =

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