Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 697 · 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 64 square m. How long is each side (in m)?
2. 2.How many whole numbers lie between 12² and 13²?
3. 3.Which of these is a perfect square? (a) 289 (b) 320 (c) 297
4. 4.What is the smallest whole number by which 48 must be divided to get a perfect square?
5. 5.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 69²? =
7. 7.A square garden has an area of 729 square m. How long is each side (in m)?
8. 8.What is √8464? =
9. 9.What is √1089? =
10. 10.How many whole numbers lie between 8² and 9²?
11. 11.What is √3600? =
12. 12.How many whole numbers lie between 45² and 46²?
13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √6561? =
15. 15.How many whole numbers lie between 22² and 23²?
16. 16.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
17. 17.What is 78²? =
18. 18.A square garden has an area of 169 square m. How long is each side (in m)?
19. 19.What is 87²? =
20. 20.A square garden has an area of 3600 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
22. 22.What is the smallest whole number by which 539 must be divided to get a perfect square?
23. 23.What is 81²? =
24. 24.Which of these is a perfect square? (a) 668 (b) 625 (c) 657
25. 25.A square garden has an area of 2809 square m. How long is each side (in m)?
26. 26.What is 72²? =
27. 27.What is √196? =
28. 28.Which of these is a perfect square? (a) 156 (b) 165 (c) 144
29. 29.What is √9216? =
30. 30.What is 95²? =
31. 31.A square garden has an area of 900 square m. How long is each side (in m)?
32. 32.A square garden has an area of 2116 square m. How long is each side (in m)?
33. 33.What is √6084? =
34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 25²? =
36. 36.How many whole numbers lie between 33² and 34²?
37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √441? =
39. 39.What is 27²? =
40. 40.How many whole numbers lie between 14² and 15²?

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