Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 511 · 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 √1600? =
2. 2.What is √5625? =
3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 63²? =
6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
7. 7.How many whole numbers lie between 45² and 46²?
8. 8.What is √1849? =
9. 9.How many whole numbers lie between 17² and 18²?
10. 10.What is 47²? =
11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
13. 13.How many whole numbers lie between 10² and 11²?
14. 14.A square garden has an area of 36 square m. How long is each side (in m)?
15. 15.What is the smallest whole number by which 44 must be divided to get a perfect square?
16. 16.A square garden has an area of 3600 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 5² and 6²?
18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 76²? =
20. 20.What is 26²? =
21. 21.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
22. 22.What is √1225? =
23. 23.A square garden has an area of 2401 square m. How long is each side (in m)?
24. 24.What is 99²? =
25. 25.How many whole numbers lie between 29² and 30²?
26. 26.Which of these is a perfect square? (a) 904 (b) 900 (c) 921
27. 27.How many whole numbers lie between 25² and 26²?
28. 28.What is 38²? =
29. 29.What is √6400? =
30. 30.A square garden has an area of 2116 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 1053 must be divided to get a perfect square?
32. 32.What is 11²? =
33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
35. 35.A square garden has an area of 2809 square m. How long is each side (in m)?
36. 36.Which of these is a perfect square? (a) 106 (b) 100 (c) 107
37. 37.How many whole numbers lie between 7² and 8²?
38. 38.A square garden has an area of 1089 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 43² and 44²?
40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?

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