Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 211 · 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) 484 (b) 485 (c) 516
2. 2.Which of these is a perfect square? (a) 1248 (b) 1225 (c) 1275
3. 3.What is √8649? =
4. 4.What is √8100? =
5. 5.How many whole numbers lie between 13² and 14²?
6. 6.A square garden has an area of 961 square m. How long is each side (in m)?
7. 7.A square garden has an area of 576 square m. How long is each side (in m)?
8. 8.What is 53²? =
9. 9.What is √676? =
10. 10.What is √4096? =
11. 11.Which of these is a perfect square? (a) 324 (b) 350 (c) 338
12. 12.What is 32²? =
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
14. 14.How many whole numbers lie between 43² and 44²?
15. 15.Which of these is a perfect square? (a) 402 (b) 424 (c) 400
16. 16.Which of these is a perfect square? (a) 115 (b) 100 (c) 106
17. 17.How many whole numbers lie between 5² and 6²?
18. 18.What is 18²? =
19. 19.How many whole numbers lie between 9² and 10²?
20. 20.What is 40²? =
21. 21.What is √361? =
22. 22.What is 64²? =
23. 23.What is √256? =
24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √144? =
26. 26.What is the smallest whole number by which 135 must be divided to get a perfect square?
27. 27.What is 26²? =
28. 28.What is 12²? =
29. 29.What is 24²? =
30. 30.What is √6400? =
31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
33. 33.A square garden has an area of 256 square m. How long is each side (in m)?
34. 34.A square garden has an area of 625 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 167 (b) 153 (c) 144
36. 36.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
37. 37.What is the smallest whole number by which 60 must be divided to get a perfect square?
38. 38.Which of these is a perfect square? (a) 175 (b) 169 (c) 171
39. 39.A square garden has an area of 121 square m. How long is each side (in m)?
40. 40.What is 65²? =

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