Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 11 · 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 3364 square m. How long is each side (in m)?
2. 2.Which of these is a perfect square? (a) 289 (b) 297 (c) 317
3. 3.What is √1521? =
4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √576? =
7. 7.Which of these is a perfect square? (a) 625 (b) 632 (c) 665
8. 8.What is √4900? =
9. 9.How many whole numbers lie between 38² and 39²?
10. 10.Which of these is a perfect square? (a) 246 (b) 235 (c) 225
11. 11.A square garden has an area of 144 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 2401 square m. How long is each side (in m)?
14. 14.What is √3969? =
15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 456 (b) 451 (c) 441
17. 17.What is √5625? =
18. 18.How many whole numbers lie between 19² and 20²?
19. 19.What is √2025? =
20. 20.What is 57²? =
21. 21.What is 15²? =
22. 22.What is the smallest whole number by which 44 must be divided to get a perfect square?
23. 23.What is 50²? =
24. 24.What is 12²? =
25. 25.What is √225? =
26. 26.A square garden has an area of 1849 square m. How long is each side (in m)?
27. 27.What is the smallest whole number by which 176 must be divided to get a perfect square?
28. 28.Which of these is a perfect square? (a) 1018 (b) 995 (c) 961
29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √900? =
31. 31.What is √1936? =
32. 32.How many whole numbers lie between 50² and 51²?
33. 33.What is 79²? =
34. 34.What is the smallest whole number by which 539 must be divided to get a perfect square?
35. 35.Which of these is a perfect square? (a) 121 (b) 139 (c) 143
36. 36.What is √1225? =
37. 37.A square garden has an area of 49 square m. How long is each side (in m)?
38. 38.What is √6241? =
39. 39.What is √9409? =
40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

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