Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 50 · 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 2704 square m. How long is each side (in m)?
2. 2.What is 55²? =
3. 3.How many whole numbers lie between 38² and 39²?
4. 4.What is √7056? =
5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 85²? =
7. 7.What is 61²? =
8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
10. 10.How many whole numbers lie between 13² and 14²?
11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √256? =
14. 14.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
15. 15.How many whole numbers lie between 12² and 13²?
16. 16.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
17. 17.How many whole numbers lie between 28² and 29²?
18. 18.What is 23²? =
19. 19.A square garden has an area of 400 square m. How long is each side (in m)?
20. 20.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 484 (b) 528 (c) 495
22. 22.What is the smallest whole number by which 162 must be divided to get a perfect square?
23. 23.What is √1444? =
24. 24.How many whole numbers lie between 29² and 30²?
25. 25.What is 26²? =
26. 26.What is √5476? =
27. 27.What is 34²? =
28. 28.How many whole numbers lie between 44² and 45²?
29. 29.What is √441? =
30. 30.Which of these is a perfect square? (a) 446 (b) 445 (c) 441
31. 31.What is the smallest whole number by which 135 must be divided to get a perfect square?
32. 32.What is 58²? =
33. 33.What is 62²? =
34. 34.What is √361? =
35. 35.What is √529? =
36. 36.What is √8464? =
37. 37.How many whole numbers lie between 45² and 46²?
38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 78²? =
40. 40.Which of these is a perfect square? (a) 235 (b) 225 (c) 245

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