Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 391 · 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.How many whole numbers lie between 7² and 8²?
2. 2.What is 62²? =
3. 3.A square garden has an area of 256 square m. How long is each side (in m)?
4. 4.How many whole numbers lie between 13² and 14²?
5. 5.What is √2209? =
6. 6.What is 21²? =
7. 7.Which of these is a perfect square? (a) 1054 (b) 1067 (c) 1024
8. 8.What is 72²? =
9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 40²? =
11. 11.What is 34²? =
12. 12.What is 73²? =
13. 13.Which of these is a perfect square? (a) 821 (b) 794 (c) 784
14. 14.What is 71²? =
15. 15.What is the smallest whole number by which 98 must be divided to get a perfect square?
16. 16.A square garden has an area of 2304 square m. How long is each side (in m)?
17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √625? =
19. 19.How many whole numbers lie between 22² and 23²?
20. 20.How many whole numbers lie between 11² and 12²?
21. 21.Which of these is a perfect square? (a) 1444 (b) 1504 (c) 1512
22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 47²? =
24. 24.A square garden has an area of 576 square m. How long is each side (in m)?
25. 25.What is √1156? =
26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the smallest whole number by which 135 must be divided to get a perfect square?
28. 28.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 64²? =
30. 30.What is √8836? =
31. 31.What is √289? =
32. 32.What is √7921? =
33. 33.How many whole numbers lie between 34² and 35²?
34. 34.Which of these is a perfect square? (a) 342 (b) 324 (c) 328
35. 35.Which of these is a perfect square? (a) 428 (b) 408 (c) 400
36. 36.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
37. 37.A square garden has an area of 1681 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 49² and 50²?
39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?

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