Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 37 · 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.Which of these is a perfect square? (a) 1299 (b) 1296 (c) 1313
2. 2.Which of these is a perfect square? (a) 484 (b) 496 (c) 494
3. 3.What is √5329? =
4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the smallest whole number by which 1053 must be divided to get a perfect square?
6. 6.Which of these is a perfect square? (a) 676 (b) 693 (c) 697
7. 7.Which of these is a perfect square? (a) 1155 (b) 1100 (c) 1089
8. 8.What is 79²? =
9. 9.What is 93²? =
10. 10.A square garden has an area of 784 square m. How long is each side (in m)?
11. 11.Which of these is a perfect square? (a) 1375 (b) 1369 (c) 1434
12. 12.How many whole numbers lie between 36² and 37²?
13. 13.What is the smallest whole number by which 735 must be divided to get a perfect square?
14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
16. 16.What is √1156? =
17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √2704? =
20. 20.What is 84²? =
21. 21.What is √289? =
22. 22.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
23. 23.What is the smallest whole number by which 490 must be divided to get a perfect square?
24. 24.What is 31²? =
25. 25.A square garden has an area of 729 square m. How long is each side (in m)?
26. 26.What is 61²? =
27. 27.What is √2809? =
28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
29. 29.What is √3481? =
30. 30.A square garden has an area of 3364 square m. How long is each side (in m)?
31. 31.What is 17²? =
32. 32.What is 41²? =
33. 33.How many whole numbers lie between 42² and 43²?
34. 34.A square garden has an area of 25 square m. How long is each side (in m)?
35. 35.What is √529? =
36. 36.A square garden has an area of 121 square m. How long is each side (in m)?
37. 37.What is √8100? =
38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
39. 39.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
40. 40.How many whole numbers lie between 21² and 22²?

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