Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 544 · 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 √361? =
2. 2.What is √4624? =
3. 3.A square garden has an area of 3481 square m. How long is each side (in m)?
4. 4.How many whole numbers lie between 20² and 21²?
5. 5.Which of these is a perfect square? (a) 474 (b) 441 (c) 442
6. 6.What is 74²? =
7. 7.What is the smallest whole number by which 135 must be divided to get a perfect square?
8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 38²? =
10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 324 (b) 338 (c) 334
12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 35² and 36²?
14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 16² and 17²?
17. 17.What is 49²? =
18. 18.Which of these is a perfect square? (a) 286 (b) 264 (c) 256
19. 19.What is √5184? =
20. 20.How many whole numbers lie between 37² and 38²?
21. 21.What is √9216? =
22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 57²? =
24. 24.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
25. 25.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
26. 26.What is 15²? =
27. 27.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
28. 28.How many whole numbers lie between 15² and 16²?
29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
30. 30.A square garden has an area of 625 square m. How long is each side (in m)?
31. 31.What is √196? =
32. 32.A square garden has an area of 784 square m. How long is each side (in m)?
33. 33.A square garden has an area of 961 square m. How long is each side (in m)?
34. 34.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
35. 35.How many whole numbers lie between 50² and 51²?
36. 36.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
37. 37.A square garden has an area of 121 square m. How long is each side (in m)?
38. 38.What is √729? =
39. 39.What is √8464? =
40. 40.What is √1764? =

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