Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 566 · 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 √3481? =
2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 12²? =
4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 2704 square m. How long is each side (in m)?
6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 256 (b) 275 (c) 270
8. 8.Which of these is a perfect square? (a) 625 (b) 638 (c) 656
9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the smallest whole number by which 147 must be divided to get a perfect square?
11. 11.Which of these is a perfect square? (a) 1304 (b) 1296 (c) 1312
12. 12.How many whole numbers lie between 37² and 38²?
13. 13.What is the smallest whole number by which 468 must be multiplied 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 54 must be divided to get a perfect square?
16. 16.A square garden has an area of 784 square m. How long is each side (in m)?
17. 17.A square garden has an area of 1521 square m. How long is each side (in m)?
18. 18.What is √8281? =
19. 19.What is √7396? =
20. 20.What is 62²? =
21. 21.Which of these is a perfect square? (a) 1600 (b) 1659 (c) 1601
22. 22.Which of these is a perfect square? (a) 1375 (b) 1402 (c) 1369
23. 23.What is 18²? =
24. 24.How many whole numbers lie between 39² and 40²?
25. 25.How many whole numbers lie between 12² and 13²?
26. 26.Which of these is a perfect square? (a) 376 (b) 361 (c) 395
27. 27.A square garden has an area of 3136 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 11² and 12²?
29. 29.What is √1089? =
30. 30.What is √6241? =
31. 31.What is 51²? =
32. 32.Which of these is a perfect square? (a) 1216 (b) 1210 (c) 1156
33. 33.A square garden has an area of 400 square m. How long is each side (in m)?
34. 34.What is 69²? =
35. 35.What is 54²? =
36. 36.What is √9604? =
37. 37.Which of these is a perfect square? (a) 225 (b) 241 (c) 234
38. 38.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
40. 40.What is 13²? =

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