Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 309 · 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 the smallest whole number by which 175 must be divided to get a perfect square?
2. 2.Which of these is a perfect square? (a) 324 (b) 330 (c) 326
3. 3.What is √4761? =
4. 4.What is 83²? =
5. 5.A square garden has an area of 121 square m. How long is each side (in m)?
6. 6.How many whole numbers lie between 12² and 13²?
7. 7.How many whole numbers lie between 36² and 37²?
8. 8.How many whole numbers lie between 5² and 6²?
9. 9.How many whole numbers lie between 45² and 46²?
10. 10.Which of these is a perfect square? (a) 398 (b) 379 (c) 361
11. 11.How many whole numbers lie between 47² and 48²?
12. 12.What is 77²? =
13. 13.Which of these is a perfect square? (a) 196 (b) 213 (c) 197
14. 14.What is 72²? =
15. 15.What is 51²? =
16. 16.What is the smallest whole number by which 468 must be divided to get a perfect square?
17. 17.What is 36²? =
18. 18.What is √1764? =
19. 19.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
20. 20.How many whole numbers lie between 39² and 40²?
21. 21.What is 43²? =
22. 22.What is √4356? =
23. 23.How many whole numbers lie between 10² and 11²?
24. 24.How many whole numbers lie between 21² and 22²?
25. 25.What is the smallest whole number by which 216 must be divided to get a perfect square?
26. 26.What is 44²? =
27. 27.How many whole numbers lie between 14² and 15²?
28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 40²? =
30. 30.What is 76²? =
31. 31.What is √3025? =
32. 32.What is 39²? =
33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
36. 36.What is √2401? =
37. 37.What is 75²? =
38. 38.What is 74²? =
39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 2116 square m. How long is each side (in m)?

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