Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 597 · 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) 1122 (b) 1152 (c) 1089
2. 2.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
3. 3.What is 76²? =
4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 11²? =
6. 6.What is √400? =
7. 7.A square garden has an area of 841 square m. How long is each side (in m)?
8. 8.What is √256? =
9. 9.Which of these is a perfect square? (a) 273 (b) 287 (c) 256
10. 10.What is 97²? =
11. 11.What is √2704? =
12. 12.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
13. 13.How many whole numbers lie between 10² and 11²?
14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
15. 15.Which of these is a perfect square? (a) 133 (b) 140 (c) 121
16. 16.What is √1156? =
17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
18. 18.Which of these is a perfect square? (a) 229 (b) 240 (c) 225
19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 729 (b) 774 (c) 735
21. 21.What is 12²? =
22. 22.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
23. 23.Which of these is a perfect square? (a) 976 (b) 978 (c) 961
24. 24.What is 68²? =
25. 25.A square garden has an area of 529 square m. How long is each side (in m)?
26. 26.A square garden has an area of 2209 square m. How long is each side (in m)?
27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 624 (b) 623 (c) 576
29. 29.What is 36²? =
30. 30.What is 28²? =
31. 31.Which of these is a perfect square? (a) 361 (b) 364 (c) 373
32. 32.What is √3249? =
33. 33.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 64 square m. How long is each side (in m)?
35. 35.What is 59²? =
36. 36.What is the smallest whole number by which 63 must be divided to get a perfect square?
37. 37.How many whole numbers lie between 23² and 24²?
38. 38.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
39. 39.How many whole numbers lie between 26² and 27²?
40. 40.What is the smallest whole number by which 176 must be multiplied to get a perfect square?

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