Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 388 · 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 √4900? =
2. 2.What is 95²? =
3. 3.A square garden has an area of 121 square m. How long is each side (in m)?
4. 4.A square garden has an area of 25 square m. How long is each side (in m)?
5. 5.A square garden has an area of 1024 square m. How long is each side (in m)?
6. 6.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
7. 7.How many whole numbers lie between 50² and 51²?
8. 8.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 10² and 11²?
10. 10.Which of these is a perfect square? (a) 482 (b) 445 (c) 441
11. 11.Which of these is a perfect square? (a) 1089 (b) 1121 (c) 1096
12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 675 (b) 625 (c) 657
14. 14.What is 65²? =
15. 15.What is 57²? =
16. 16.What is 11²? =
17. 17.How many whole numbers lie between 35² and 36²?
18. 18.How many whole numbers lie between 36² and 37²?
19. 19.What is 83²? =
20. 20.Which of these is a perfect square? (a) 1085 (b) 1046 (c) 1024
21. 21.A square garden has an area of 841 square m. How long is each side (in m)?
22. 22.How many whole numbers lie between 9² and 10²?
23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 487 (b) 516 (c) 484
25. 25.What is 43²? =
26. 26.What is √5625? =
27. 27.What is √3364? =
28. 28.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
29. 29.What is 31²? =
30. 30.Which of these is a perfect square? (a) 178 (b) 169 (c) 174
31. 31.What is 19²? =
32. 32.What is √9216? =
33. 33.What is √3969? =
34. 34.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
35. 35.What is 37²? =
36. 36.What is √4489? =
37. 37.A square garden has an area of 2209 square m. How long is each side (in m)?
38. 38.What is 66²? =
39. 39.What is √841? =
40. 40.How many whole numbers lie between 48² and 49²?

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