Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 580 · 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 34²? =
2. 2.What is the smallest whole number by which 72 must be divided to get a perfect square?
3. 3.Which of these is a perfect square? (a) 311 (b) 289 (c) 315
4. 4.How many whole numbers lie between 5² and 6²?
5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
7. 7.A square garden has an area of 576 square m. How long is each side (in m)?
8. 8.A square garden has an area of 900 square m. How long is each side (in m)?
9. 9.What is 12²? =
10. 10.Which of these is a perfect square? (a) 248 (b) 241 (c) 225
11. 11.What is 64²? =
12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √289? =
14. 14.How many whole numbers lie between 29² and 30²?
15. 15.What is √6084? =
16. 16.How many whole numbers lie between 30² and 31²?
17. 17.What is 94²? =
18. 18.What is 17²? =
19. 19.What is 93²? =
20. 20.How many whole numbers lie between 32² and 33²?
21. 21.What is √2704? =
22. 22.How many whole numbers lie between 47² and 48²?
23. 23.What is 24²? =
24. 24.Which of these is a perfect square? (a) 523 (b) 484 (c) 487
25. 25.Which of these is a perfect square? (a) 403 (b) 424 (c) 400
26. 26.What is 45²? =
27. 27.What is √5329? =
28. 28.What is √1024? =
29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
31. 31.What is 39²? =
32. 32.Which of these is a perfect square? (a) 1524 (b) 1550 (c) 1521
33. 33.What is √2209? =
34. 34.How many whole numbers lie between 50² and 51²?
35. 35.A square garden has an area of 2809 square m. How long is each side (in m)?
36. 36.What is 26²? =
37. 37.A square garden has an area of 529 square m. How long is each side (in m)?
38. 38.What is the smallest whole number by which 126 must be divided to get a perfect square?
39. 39.How many whole numbers lie between 40² and 41²?
40. 40.What is √5625? =

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