Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 732 · 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.Which of these is a perfect square? (a) 643 (b) 625 (c) 634
2. 2.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
3. 3.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
4. 4.What is 92²? =
5. 5.What is √729? =
6. 6.A square garden has an area of 1681 square m. How long is each side (in m)?
7. 7.How many whole numbers lie between 12² and 13²?
8. 8.What is 74²? =
9. 9.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
10. 10.What is √144? =
11. 11.What is 47²? =
12. 12.Which of these is a perfect square? (a) 864 (b) 841 (c) 888
13. 13.What is √484? =
14. 14.Which of these is a perfect square? (a) 364 (b) 361 (c) 370
15. 15.A square garden has an area of 2116 square m. How long is each side (in m)?
16. 16.What is √6561? =
17. 17.What is √8100? =
18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √7056? =
20. 20.How many whole numbers lie between 9² and 10²?
21. 21.How many whole numbers lie between 5² and 6²?
22. 22.What is 12²? =
23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the smallest whole number by which 240 must be divided to get a perfect square?
25. 25.What is 27²? =
26. 26.How many whole numbers lie between 17² and 18²?
27. 27.What is 43²? =
28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 620 (b) 623 (c) 576
30. 30.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 97²? =
32. 32.How many whole numbers lie between 30² and 31²?
33. 33.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
34. 34.What is √4761? =
35. 35.How many whole numbers lie between 39² and 40²?
36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 46²? =
38. 38.What is 85²? =
39. 39.What is √8281? =
40. 40.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?

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