Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 634 · 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 the smallest whole number by which 162 must be multiplied to get a perfect square?
2. 2.A square garden has an area of 169 square m. How long is each side (in m)?
3. 3.How many whole numbers lie between 15² and 16²?
4. 4.What is √1521? =
5. 5.How many whole numbers lie between 27² and 28²?
6. 6.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
7. 7.What is 46²? =
8. 8.How many whole numbers lie between 34² and 35²?
9. 9.Which of these is a perfect square? (a) 366 (b) 361 (c) 376
10. 10.Which of these is a perfect square? (a) 1178 (b) 1157 (c) 1156
11. 11.What is √3249? =
12. 12.What is √784? =
13. 13.What is 23²? =
14. 14.A square garden has an area of 729 square m. How long is each side (in m)?
15. 15.How many whole numbers lie between 33² and 34²?
16. 16.A square garden has an area of 841 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 170 (b) 169 (c) 181
18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
20. 20.Which of these is a perfect square? (a) 685 (b) 676 (c) 710
21. 21.What is √441? =
22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 841 (b) 856 (c) 853
25. 25.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
27. 27.What is 40²? =
28. 28.A square garden has an area of 49 square m. How long is each side (in m)?
29. 29.What is 62²? =
30. 30.What is 67²? =
31. 31.Which of these is a perfect square? (a) 1331 (b) 1296 (c) 1316
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the smallest whole number by which 539 must be divided to get a perfect square?
34. 34.What is 16²? =
35. 35.What is 18²? =
36. 36.What is the smallest whole number by which 96 must be divided to get a perfect square?
37. 37.What is 49²? =
38. 38.A square garden has an area of 1600 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 6² and 7²?
40. 40.What is 75²? =

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