Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 153 · 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 729 square m. How long is each side (in m)?
2. 2.Which of these is a perfect square? (a) 625 (b) 638 (c) 664
3. 3.What is √2601? =
4. 4.How many whole numbers lie between 5² and 6²?
5. 5.Which of these is a perfect square? (a) 972 (b) 961 (c) 1019
6. 6.What is 18²? =
7. 7.How many whole numbers lie between 9² and 10²?
8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
9. 9.A square garden has an area of 324 square m. How long is each side (in m)?
10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
11. 11.How many whole numbers lie between 22² and 23²?
12. 12.What is the smallest whole number by which 18 must be divided to get a perfect square?
13. 13.How many whole numbers lie between 26² and 27²?
14. 14.A square garden has an area of 81 square m. How long is each side (in m)?
15. 15.A square garden has an area of 3364 square m. How long is each side (in m)?
16. 16.What is √5929? =
17. 17.Which of these is a perfect square? (a) 404 (b) 439 (c) 400
18. 18.Which of these is a perfect square? (a) 117 (b) 103 (c) 100
19. 19.What is √784? =
20. 20.What is 77²? =
21. 21.How many whole numbers lie between 49² and 50²?
22. 22.What is 59²? =
23. 23.How many whole numbers lie between 43² and 44²?
24. 24.What is the smallest whole number by which 637 must be divided to get a perfect square?
25. 25.What is √1849? =
26. 26.A square garden has an area of 1296 square m. How long is each side (in m)?
27. 27.What is 38²? =
28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 35²? =
30. 30.A square garden has an area of 169 square m. How long is each side (in m)?
31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
32. 32.What is 24²? =
33. 33.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
34. 34.A square garden has an area of 1444 square m. How long is each side (in m)?
35. 35.What is √8281? =
36. 36.What is 74²? =
37. 37.What is the smallest whole number by which 192 must be divided to get a perfect square?
38. 38.What is the smallest whole number by which 320 must be divided to get a perfect square?
39. 39.What is the smallest whole number by which 360 must be divided to get a perfect square?
40. 40.Which of these is a perfect square? (a) 784 (b) 803 (c) 790

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