Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 358 · 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 14² and 15²?
2. 2.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
3. 3.What is √121? =
4. 4.A square garden has an area of 2809 square m. How long is each side (in m)?
5. 5.A square garden has an area of 196 square m. How long is each side (in m)?
6. 6.A square garden has an area of 625 square m. How long is each side (in m)?
7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
8. 8.Which of these is a perfect square? (a) 264 (b) 269 (c) 256
9. 9.What is √8464? =
10. 10.How many whole numbers lie between 32² and 33²?
11. 11.Which of these is a perfect square? (a) 196 (b) 221 (c) 199
12. 12.How many whole numbers lie between 17² and 18²?
13. 13.Which of these is a perfect square? (a) 545 (b) 573 (c) 529
14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
15. 15.A square garden has an area of 1849 square m. How long is each side (in m)?
16. 16.What is √5476? =
17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
18. 18.What is 93²? =
19. 19.What is √256? =
20. 20.What is √3844? =
21. 21.Which of these is a perfect square? (a) 502 (b) 525 (c) 484
22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the smallest whole number by which 52 must be divided to get a perfect square?
25. 25.Which of these is a perfect square? (a) 373 (b) 396 (c) 361
26. 26.What is 54²? =
27. 27.What is √9025? =
28. 28.A square garden has an area of 2401 square m. How long is each side (in m)?
29. 29.What is √289? =
30. 30.What is 88²? =
31. 31.Which of these is a perfect square? (a) 729 (b) 730 (c) 744
32. 32.What is √784? =
33. 33.A square garden has an area of 36 square m. How long is each side (in m)?
34. 34.A square garden has an area of 2209 square m. How long is each side (in m)?
35. 35.What is √8281? =
36. 36.Which of these is a perfect square? (a) 1643 (b) 1600 (c) 1609
37. 37.What is 79²? =
38. 38.What is √6241? =
39. 39.What is 44²? =
40. 40.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?

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