Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 400 · 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 √2304? =
2. 2.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √9025? =
4. 4.What is 48²? =
5. 5.Which of these is a perfect square? (a) 686 (b) 684 (c) 676
6. 6.What is 94²? =
7. 7.A square garden has an area of 784 square m. How long is each side (in m)?
8. 8.How many whole numbers lie between 37² and 38²?
9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 33²? =
11. 11.How many whole numbers lie between 10² and 11²?
12. 12.What is 50²? =
13. 13.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
15. 15.Which of these is a perfect square? (a) 1654 (b) 1631 (c) 1600
16. 16.How many whole numbers lie between 39² and 40²?
17. 17.What is √7921? =
18. 18.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
19. 19.How many whole numbers lie between 15² and 16²?
20. 20.Which of these is a perfect square? (a) 1444 (b) 1457 (c) 1481
21. 21.What is 32²? =
22. 22.What is 61²? =
23. 23.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
24. 24.What is √6084? =
25. 25.Which of these is a perfect square? (a) 536 (b) 567 (c) 529
26. 26.What is 73²? =
27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
29. 29.What is the smallest whole number by which 52 must be divided to get a perfect square?
30. 30.What is 17²? =
31. 31.What is the smallest whole number by which 108 must be divided to get a perfect square?
32. 32.How many whole numbers lie between 30² and 31²?
33. 33.A square garden has an area of 64 square m. How long is each side (in m)?
34. 34.How many whole numbers lie between 13² and 14²?
35. 35.How many whole numbers lie between 12² and 13²?
36. 36.What is √3249? =
37. 37.What is √1600? =
38. 38.Which of these is a perfect square? (a) 1584 (b) 1596 (c) 1521
39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
40. 40.What is the smallest whole number by which 96 must be divided to get a perfect square?

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