Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 368 · 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 √2401? =
2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √3364? =
4. 4.What is 33²? =
5. 5.Which of these is a perfect square? (a) 1600 (b) 1646 (c) 1655
6. 6.Which of these is a perfect square? (a) 140 (b) 121 (c) 130
7. 7.Which of these is a perfect square? (a) 961 (b) 994 (c) 1004
8. 8.A square garden has an area of 256 square m. How long is each side (in m)?
9. 9.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
10. 10.How many whole numbers lie between 15² and 16²?
11. 11.What is 84²? =
12. 12.What is the smallest whole number by which 99 must be divided to get a perfect square?
13. 13.How many whole numbers lie between 9² and 10²?
14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
16. 16.Which of these is a perfect square? (a) 165 (b) 160 (c) 144
17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √1225? =
19. 19.Which of these is a perfect square? (a) 576 (b) 610 (c) 585
20. 20.What is √4489? =
21. 21.How many whole numbers lie between 44² and 45²?
22. 22.What is 11²? =
23. 23.What is √2809? =
24. 24.A square garden has an area of 49 square m. How long is each side (in m)?
25. 25.What is √196? =
26. 26.A square garden has an area of 121 square m. How long is each side (in m)?
27. 27.What is √1024? =
28. 28.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
29. 29.Which of these is a perfect square? (a) 1402 (b) 1391 (c) 1369
30. 30.How many whole numbers lie between 27² and 28²?
31. 31.What is √6561? =
32. 32.A square garden has an area of 1521 square m. How long is each side (in m)?
33. 33.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
34. 34.What is √9216? =
35. 35.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
36. 36.What is 66²? =
37. 37.What is 96²? =
38. 38.What is √6400? =
39. 39.Which of these is a perfect square? (a) 551 (b) 542 (c) 529
40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?

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