Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 235 · 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 67²? =
2. 2.What is 13²? =
3. 3.A square garden has an area of 625 square m. How long is each side (in m)?
4. 4.What is 72²? =
5. 5.Which of these is a perfect square? (a) 636 (b) 658 (c) 625
6. 6.What is 62²? =
7. 7.How many whole numbers lie between 9² and 10²?
8. 8.What is 51²? =
9. 9.What is 28²? =
10. 10.What is 64²? =
11. 11.What is 97²? =
12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √5776? =
15. 15.How many whole numbers lie between 25² and 26²?
16. 16.Which of these is a perfect square? (a) 441 (b) 466 (c) 455
17. 17.How many whole numbers lie between 7² and 8²?
18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
21. 21.Which of these is a perfect square? (a) 676 (b) 700 (c) 706
22. 22.What is 95²? =
23. 23.A square garden has an area of 324 square m. How long is each side (in m)?
24. 24.What is √196? =
25. 25.How many whole numbers lie between 5² and 6²?
26. 26.What is 43²? =
27. 27.What is 83²? =
28. 28.How many whole numbers lie between 6² and 7²?
29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 224 must be divided to get a perfect square?
33. 33.What is √441? =
34. 34.How many whole numbers lie between 37² and 38²?
35. 35.How many whole numbers lie between 11² and 12²?
36. 36.What is 24²? =
37. 37.What is √7056? =
38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √8649? =
40. 40.How many whole numbers lie between 20² and 21²?

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