Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 577 · 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.A square garden has an area of 2916 square m. How long is each side (in m)?
2. 2.How many whole numbers lie between 32² and 33²?
3. 3.What is 23²? =
4. 4.What is 75²? =
5. 5.What is 24²? =
6. 6.What is 20²? =
7. 7.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
10. 10.What is √7396? =
11. 11.What is √625? =
12. 12.What is the smallest whole number by which 637 must be divided to get a perfect square?
13. 13.How many whole numbers lie between 31² and 32²?
14. 14.Which of these is a perfect square? (a) 576 (b) 594 (c) 582
15. 15.What is 22²? =
16. 16.What is 60²? =
17. 17.How many whole numbers lie between 7² and 8²?
18. 18.What is √1089? =
19. 19.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
20. 20.What is 36²? =
21. 21.How many whole numbers lie between 45² and 46²?
22. 22.What is √2809? =
23. 23.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
24. 24.What is 96²? =
25. 25.What is 19²? =
26. 26.How many whole numbers lie between 20² and 21²?
27. 27.What is 42²? =
28. 28.What is √1156? =
29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √3844? =
31. 31.How many whole numbers lie between 46² and 47²?
32. 32.How many whole numbers lie between 34² and 35²?
33. 33.What is 15²? =
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 40² and 41²?
36. 36.A square garden has an area of 144 square m. How long is each side (in m)?
37. 37.How many whole numbers lie between 33² and 34²?
38. 38.Which of these is a perfect square? (a) 1061 (b) 1024 (c) 1032
39. 39.What is 81²? =
40. 40.Which of these is a perfect square? (a) 221 (b) 196 (c) 212

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets