Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 495 · 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 √7056? =
2. 2.What is 67²? =
3. 3.A square garden has an area of 1024 square m. How long is each side (in m)?
4. 4.A square garden has an area of 81 square m. How long is each side (in m)?
5. 5.Which of these is a perfect square? (a) 1024 (b) 1044 (c) 1053
6. 6.What is 87²? =
7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √225? =
9. 9.What is √1764? =
10. 10.What is 45²? =
11. 11.Which of these is a perfect square? (a) 729 (b) 776 (c) 737
12. 12.What is √1296? =
13. 13.What is √9025? =
14. 14.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
15. 15.What is the smallest whole number by which 176 must be divided to get a perfect square?
16. 16.A square garden has an area of 1089 square m. How long is each side (in m)?
17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 16² and 17²?
19. 19.Which of these is a perfect square? (a) 260 (b) 272 (c) 256
20. 20.What is √5041? =
21. 21.How many whole numbers lie between 37² and 38²?
22. 22.Which of these is a perfect square? (a) 196 (b) 198 (c) 224
23. 23.What is 65²? =
24. 24.What is √8464? =
25. 25.What is 13²? =
26. 26.How many whole numbers lie between 11² and 12²?
27. 27.A square garden has an area of 169 square m. How long is each side (in m)?
28. 28.What is √6084? =
29. 29.Which of these is a perfect square? (a) 1318 (b) 1296 (c) 1368
30. 30.How many whole numbers lie between 38² and 39²?
31. 31.Which of these is a perfect square? (a) 252 (b) 225 (c) 228
32. 32.How many whole numbers lie between 40² and 41²?
33. 33.What is 46²? =
34. 34.A square garden has an area of 49 square m. How long is each side (in m)?
35. 35.What is √5476? =
36. 36.Which of these is a perfect square? (a) 1622 (b) 1680 (c) 1600
37. 37.What is 33²? =
38. 38.What is √3136? =
39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
40. 40.A square garden has an area of 2916 square m. How long is each side (in m)?

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