Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 477 · 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 the smallest whole number by which 75 must be multiplied to get a perfect square?
2. 2.How many whole numbers lie between 11² and 12²?
3. 3.Which of these is a perfect square? (a) 692 (b) 689 (c) 676
4. 4.What is √2500? =
5. 5.Which of these is a perfect square? (a) 1646 (b) 1600 (c) 1610
6. 6.What is 87²? =
7. 7.What is 36²? =
8. 8.Which of these is a perfect square? (a) 643 (b) 647 (c) 625
9. 9.How many whole numbers lie between 30² and 31²?
10. 10.A square garden has an area of 196 square m. How long is each side (in m)?
11. 11.What is √625? =
12. 12.A square garden has an area of 1764 square m. How long is each side (in m)?
13. 13.What is 43²? =
14. 14.What is √1225? =
15. 15.What is √1849? =
16. 16.How many whole numbers lie between 17² and 18²?
17. 17.What is 76²? =
18. 18.Which of these is a perfect square? (a) 119 (b) 114 (c) 100
19. 19.What is √961? =
20. 20.Which of these is a perfect square? (a) 609 (b) 599 (c) 576
21. 21.Which of these is a perfect square? (a) 910 (b) 955 (c) 900
22. 22.A square garden has an area of 100 square m. How long is each side (in m)?
23. 23.What is 42²? =
24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
25. 25.What is 93²? =
26. 26.A square garden has an area of 2025 square m. How long is each side (in m)?
27. 27.A square garden has an area of 441 square m. How long is each side (in m)?
28. 28.A square garden has an area of 3136 square m. How long is each side (in m)?
29. 29.What is √1444? =
30. 30.What is 72²? =
31. 31.What is the smallest whole number by which 637 must be divided to get a perfect square?
32. 32.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
33. 33.Which of these is a perfect square? (a) 263 (b) 256 (c) 258
34. 34.What is 48²? =
35. 35.What is √576? =
36. 36.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
37. 37.What is 28²? =
38. 38.What is 89²? =
39. 39.What is √8100? =
40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

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