Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 315 · 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 896 must be multiplied to get a perfect square?
2. 2.What is √6724? =
3. 3.A square garden has an area of 2809 square m. How long is each side (in m)?
4. 4.Which of these is a perfect square? (a) 611 (b) 609 (c) 576
5. 5.What is 19²? =
6. 6.A square garden has an area of 196 square m. How long is each side (in m)?
7. 7.A square garden has an area of 2116 square m. How long is each side (in m)?
8. 8.A square garden has an area of 2209 square m. How long is each side (in m)?
9. 9.What is 96²? =
10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 80²? =
12. 12.What is 48²? =
13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 49²? =
16. 16.What is 77²? =
17. 17.A square garden has an area of 144 square m. How long is each side (in m)?
18. 18.How many whole numbers lie between 14² and 15²?
19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 225 square m. How long is each side (in m)?
21. 21.A square garden has an area of 3025 square m. How long is each side (in m)?
22. 22.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
23. 23.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 7² and 8²?
26. 26.What is the smallest whole number by which 539 must be divided to get a perfect square?
27. 27.What is √7225? =
28. 28.How many whole numbers lie between 12² and 13²?
29. 29.How many whole numbers lie between 32² and 33²?
30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
31. 31.Which of these is a perfect square? (a) 324 (b) 339 (c) 355
32. 32.What is 39²? =
33. 33.What is 28²? =
34. 34.What is √2809? =
35. 35.Which of these is a perfect square? (a) 1458 (b) 1444 (c) 1483
36. 36.What is √5776? =
37. 37.Which of these is a perfect square? (a) 169 (b) 182 (c) 184
38. 38.What is √676? =
39. 39.What is √7744? =
40. 40.What is √1681? =

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