Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 115 · 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 89²? =
2. 2.A square garden has an area of 3364 square m. How long is each side (in m)?
3. 3.What is 70²? =
4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 14²? =
6. 6.How many whole numbers lie between 16² and 17²?
7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
9. 9.Which of these is a perfect square? (a) 400 (b) 440 (c) 407
10. 10.What is 69²? =
11. 11.What is 79²? =
12. 12.A square garden has an area of 1444 square m. How long is each side (in m)?
13. 13.What is 29²? =
14. 14.How many whole numbers lie between 12² and 13²?
15. 15.How many whole numbers lie between 44² and 45²?
16. 16.What is 72²? =
17. 17.What is √1089? =
18. 18.A square garden has an area of 625 square m. How long is each side (in m)?
19. 19.What is 34²? =
20. 20.What is 23²? =
21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 15²? =
23. 23.How many whole numbers lie between 8² and 9²?
24. 24.A square garden has an area of 324 square m. How long is each side (in m)?
25. 25.What is √5476? =
26. 26.What is 88²? =
27. 27.What is 40²? =
28. 28.What is √3600? =
29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the smallest whole number by which 640 must be divided to get a perfect square?
31. 31.What is √7921? =
32. 32.A square garden has an area of 256 square m. How long is each side (in m)?
33. 33.Which of these is a perfect square? (a) 1031 (b) 1060 (c) 1024
34. 34.A square garden has an area of 2025 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 37² and 38²?
36. 36.A square garden has an area of 1936 square m. How long is each side (in m)?
37. 37.Which of these is a perfect square? (a) 729 (b) 744 (c) 762
38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 859 (b) 841 (c) 863
40. 40.A square garden has an area of 2916 square m. How long is each side (in m)?

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