Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 239 · 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 √5041? =
2. 2.What is √6241? =
3. 3.What is 36²? =
4. 4.What is 79²? =
5. 5.What is 38²? =
6. 6.Which of these is a perfect square? (a) 666 (b) 625 (c) 663
7. 7.A square garden has an area of 64 square m. How long is each side (in m)?
8. 8.A square garden has an area of 625 square m. How long is each side (in m)?
9. 9.A square garden has an area of 2704 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 90 must be divided to get a perfect square?
11. 11.A square garden has an area of 3136 square m. How long is each side (in m)?
12. 12.How many whole numbers lie between 20² and 21²?
13. 13.What is √121? =
14. 14.A square garden has an area of 196 square m. How long is each side (in m)?
15. 15.A square garden has an area of 2116 square m. How long is each side (in m)?
16. 16.A square garden has an area of 3364 square m. How long is each side (in m)?
17. 17.What is √3721? =
18. 18.A square garden has an area of 1681 square m. How long is each side (in m)?
19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
21. 21.How many whole numbers lie between 25² and 26²?
22. 22.What is 11²? =
23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 1332 (b) 1296 (c) 1345
25. 25.Which of these is a perfect square? (a) 550 (b) 529 (c) 568
26. 26.What is 49²? =
27. 27.What is the smallest whole number by which 960 must be divided to get a perfect square?
28. 28.How many whole numbers lie between 17² and 18²?
29. 29.What is 65²? =
30. 30.A square garden has an area of 784 square m. How long is each side (in m)?
31. 31.What is 85²? =
32. 32.What is √729? =
33. 33.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
34. 34.Which of these is a perfect square? (a) 323 (b) 289 (c) 316
35. 35.How many whole numbers lie between 12² and 13²?
36. 36.What is 94²? =
37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √1225? =
40. 40.What is 83²? =

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