Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 695 · 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.A square garden has an area of 1156 square m. How long is each side (in m)?
2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √576? =
4. 4.What is 27²? =
5. 5.Which of these is a perfect square? (a) 881 (b) 841 (c) 885
6. 6.What is 87²? =
7. 7.What is 89²? =
8. 8.What is √3249? =
9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 3600 square m. How long is each side (in m)?
11. 11.What is √2500? =
12. 12.What is √324? =
13. 13.What is √2116? =
14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
16. 16.Which of these is a perfect square? (a) 1110 (b) 1113 (c) 1089
17. 17.What is √3969? =
18. 18.A square garden has an area of 1444 square m. How long is each side (in m)?
19. 19.What is √225? =
20. 20.How many whole numbers lie between 30² and 31²?
21. 21.What is 51²? =
22. 22.What is the smallest whole number by which 891 must be divided to get a perfect square?
23. 23.What is √2209? =
24. 24.What is 68²? =
25. 25.How many whole numbers lie between 33² and 34²?
26. 26.Which of these is a perfect square? (a) 784 (b) 808 (c) 799
27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 148 (b) 144 (c) 152
29. 29.Which of these is a perfect square? (a) 1436 (b) 1442 (c) 1369
30. 30.What is 65²? =
31. 31.How many whole numbers lie between 31² and 32²?
32. 32.How many whole numbers lie between 12² and 13²?
33. 33.What is 55²? =
34. 34.What is the smallest whole number by which 384 must be divided to get a perfect square?
35. 35.What is 39²? =
36. 36.Which of these is a perfect square? (a) 441 (b) 442 (c) 457
37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
38. 38.A square garden has an area of 3025 square m. How long is each side (in m)?
39. 39.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
40. 40.What is √6889? =

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