Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 451 · 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.A square garden has an area of 361 square m. How long is each side (in m)?
2. 2.What is 48²? =
3. 3.What is √1089? =
4. 4.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 65²? =
7. 7.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
8. 8.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 20² and 21²?
10. 10.Which of these is a perfect square? (a) 555 (b) 529 (c) 570
11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
12. 12.How many whole numbers lie between 7² and 8²?
13. 13.What is 23²? =
14. 14.What is 83²? =
15. 15.A square garden has an area of 1849 square m. How long is each side (in m)?
16. 16.How many whole numbers lie between 5² and 6²?
17. 17.How many whole numbers lie between 38² and 39²?
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 441 (b) 443 (c) 453
20. 20.What is √9409? =
21. 21.How many whole numbers lie between 49² and 50²?
22. 22.What is 62²? =
23. 23.What is 73²? =
24. 24.How many whole numbers lie between 46² and 47²?
25. 25.How many whole numbers lie between 10² and 11²?
26. 26.Which of these is a perfect square? (a) 668 (b) 625 (c) 650
27. 27.How many whole numbers lie between 37² and 38²?
28. 28.What is √784? =
29. 29.What is √2116? =
30. 30.What is √121? =
31. 31.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
32. 32.What is √8836? =
33. 33.Which of these is a perfect square? (a) 330 (b) 342 (c) 324
34. 34.What is 99²? =
35. 35.A square garden has an area of 225 square m. How long is each side (in m)?
36. 36.What is 36²? =
37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
39. 39.What is √6241? =
40. 40.What is 88²? =

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