Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 441 · 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 √3249? =
2. 2.What is √7396? =
3. 3.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
4. 4.Which of these is a perfect square? (a) 834 (b) 784 (c) 818
5. 5.How many whole numbers lie between 47² and 48²?
6. 6.What is √1024? =
7. 7.Which of these is a perfect square? (a) 509 (b) 484 (c) 507
8. 8.A square garden has an area of 2209 square m. How long is each side (in m)?
9. 9.Which of these is a perfect square? (a) 1156 (b) 1187 (c) 1196
10. 10.A square garden has an area of 25 square m. How long is each side (in m)?
11. 11.What is √4624? =
12. 12.What is the smallest whole number by which 54 must be divided to get a perfect square?
13. 13.What is 68²? =
14. 14.Which of these is a perfect square? (a) 430 (b) 409 (c) 400
15. 15.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
16. 16.A square garden has an area of 3600 square m. How long is each side (in m)?
17. 17.What is √8649? =
18. 18.Which of these is a perfect square? (a) 544 (b) 549 (c) 529
19. 19.What is 82²? =
20. 20.A square garden has an area of 256 square m. How long is each side (in m)?
21. 21.How many whole numbers lie between 45² and 46²?
22. 22.What is √5041? =
23. 23.A square garden has an area of 1444 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 900 (b) 907 (c) 922
25. 25.Which of these is a perfect square? (a) 1474 (b) 1444 (c) 1493
26. 26.What is √7056? =
27. 27.Which of these is a perfect square? (a) 640 (b) 659 (c) 625
28. 28.What is √9409? =
29. 29.How many whole numbers lie between 13² and 14²?
30. 30.A square garden has an area of 121 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 1296 (b) 1362 (c) 1361
32. 32.Which of these is a perfect square? (a) 144 (b) 153 (c) 162
33. 33.What is the smallest whole number by which 160 must be divided to get a perfect square?
34. 34.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
35. 35.What is 26²? =
36. 36.How many whole numbers lie between 40² and 41²?
37. 37.What is 49²? =
38. 38.What is 40²? =
39. 39.What is √7744? =
40. 40.What is 85²? =

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