Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 512 · 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 √2704? =
2. 2.What is √6561? =
3. 3.Which of these is a perfect square? (a) 612 (b) 576 (c) 585
4. 4.What is √2025? =
5. 5.How many whole numbers lie between 49² and 50²?
6. 6.What is √4356? =
7. 7.How many whole numbers lie between 10² and 11²?
8. 8.A square garden has an area of 1156 square m. How long is each side (in m)?
9. 9.What is the smallest whole number by which 27 must be divided to get a perfect square?
10. 10.What is 41²? =
11. 11.What is 79²? =
12. 12.What is 35²? =
13. 13.A square garden has an area of 289 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 444 (b) 472 (c) 441
15. 15.What is the smallest whole number by which 80 must be divided to get a perfect square?
16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
17. 17.A square garden has an area of 625 square m. How long is each side (in m)?
18. 18.Which of these is a perfect square? (a) 329 (b) 324 (c) 339
19. 19.How many whole numbers lie between 31² and 32²?
20. 20.How many whole numbers lie between 42² and 43²?
21. 21.Which of these is a perfect square? (a) 484 (b) 524 (c) 490
22. 22.What is 51²? =
23. 23.What is 28²? =
24. 24.A square garden has an area of 3136 square m. How long is each side (in m)?
25. 25.What is the smallest whole number by which 96 must be divided to get a perfect square?
26. 26.A square garden has an area of 100 square m. How long is each side (in m)?
27. 27.What is √1296? =
28. 28.Which of these is a perfect square? (a) 971 (b) 961 (c) 986
29. 29.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
30. 30.How many whole numbers lie between 20² and 21²?
31. 31.A square garden has an area of 49 square m. How long is each side (in m)?
32. 32.What is 48²? =
33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 18² and 19²?
35. 35.How many whole numbers lie between 14² and 15²?
36. 36.What is √1681? =
37. 37.What is 43²? =
38. 38.A square garden has an area of 400 square m. How long is each side (in m)?
39. 39.What is 65²? =
40. 40.A square garden has an area of 841 square m. How long is each side (in m)?

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