Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 76 · 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 33²? =
2. 2.What is √1024? =
3. 3.What is √9216? =
4. 4.Which of these is a perfect square? (a) 266 (b) 277 (c) 256
5. 5.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
6. 6.What is 39²? =
7. 7.What is √6724? =
8. 8.What is √625? =
9. 9.What is the smallest whole number by which 125 must be divided to get a perfect square?
10. 10.What is 59²? =
11. 11.What is 21²? =
12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
14. 14.A square garden has an area of 25 square m. How long is each side (in m)?
15. 15.What is √6241? =
16. 16.Which of these is a perfect square? (a) 576 (b) 584 (c) 579
17. 17.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
18. 18.How many whole numbers lie between 11² and 12²?
19. 19.What is the smallest whole number by which 360 must be divided to get a perfect square?
20. 20.What is 35²? =
21. 21.A square garden has an area of 225 square m. How long is each side (in m)?
22. 22.A square garden has an area of 3481 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 977 (b) 961 (c) 984
24. 24.What is √2401? =
25. 25.What is the smallest whole number by which 108 must be divided to get a perfect square?
26. 26.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 1239 (b) 1225 (c) 1241
29. 29.Which of these is a perfect square? (a) 529 (b) 572 (c) 549
30. 30.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
31. 31.What is √8281? =
32. 32.Which of these is a perfect square? (a) 676 (b) 686 (c) 712
33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 3025 square m. How long is each side (in m)?
35. 35.What is the smallest whole number by which 704 must be divided to get a perfect square?
36. 36.What is the smallest whole number by which 150 must be divided to get a perfect square?
37. 37.Which of these is a perfect square? (a) 885 (b) 860 (c) 841
38. 38.What is 22²? =
39. 39.Which of these is a perfect square? (a) 191 (b) 169 (c) 188
40. 40.What is the smallest whole number by which 24 must be multiplied to get a perfect square?

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