Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 92 · 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.How many whole numbers lie between 47² and 48²?
2. 2.What is √2809? =
3. 3.Which of these is a perfect square? (a) 132 (b) 129 (c) 121
4. 4.What is 32²? =
5. 5.A square garden has an area of 1849 square m. How long is each side (in m)?
6. 6.Which of these is a perfect square? (a) 325 (b) 324 (c) 357
7. 7.What is √1296? =
8. 8.A square garden has an area of 1681 square m. How long is each side (in m)?
9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
11. 11.What is 66²? =
12. 12.What is 70²? =
13. 13.What is √5776? =
14. 14.What is 22²? =
15. 15.What is √9801? =
16. 16.How many whole numbers lie between 49² and 50²?
17. 17.Which of these is a perfect square? (a) 1598 (b) 1521 (c) 1589
18. 18.Which of these is a perfect square? (a) 841 (b) 853 (c) 874
19. 19.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
20. 20.What is √3969? =
21. 21.What is the smallest whole number by which 28 must be divided to get a perfect square?
22. 22.What is √3481? =
23. 23.What is 31²? =
24. 24.A square garden has an area of 169 square m. How long is each side (in m)?
25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
26. 26.What is √4356? =
27. 27.How many whole numbers lie between 7² and 8²?
28. 28.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
29. 29.What is √484? =
30. 30.A square garden has an area of 961 square m. How long is each side (in m)?
31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √9604? =
34. 34.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
35. 35.How many whole numbers lie between 6² and 7²?
36. 36.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
37. 37.Which of these is a perfect square? (a) 400 (b) 422 (c) 411
38. 38.What is the smallest whole number by which 98 must be divided to get a perfect square?
39. 39.Which of these is a perfect square? (a) 255 (b) 241 (c) 225
40. 40.What is the smallest whole number by which 250 must be divided to get a perfect square?

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