Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 60 · 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 29² and 30²?
2. 2.What is √6241? =
3. 3.Which of these is a perfect square? (a) 1199 (b) 1207 (c) 1156
4. 4.A square garden has an area of 2116 square m. How long is each side (in m)?
5. 5.What is √1024? =
6. 6.What is 14²? =
7. 7.What is √3600? =
8. 8.What is √2916? =
9. 9.How many whole numbers lie between 24² and 25²?
10. 10.What is √2704? =
11. 11.What is √7056? =
12. 12.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
13. 13.What is 35²? =
14. 14.How many whole numbers lie between 10² and 11²?
15. 15.What is 13²? =
16. 16.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
17. 17.What is √7921? =
18. 18.A square garden has an area of 676 square m. How long is each side (in m)?
19. 19.What is √5476? =
20. 20.How many whole numbers lie between 13² and 14²?
21. 21.Which of these is a perfect square? (a) 416 (b) 403 (c) 400
22. 22.A square garden has an area of 3600 square m. How long is each side (in m)?
23. 23.What is √8281? =
24. 24.What is 49²? =
25. 25.What is 69²? =
26. 26.What is √484? =
27. 27.What is 77²? =
28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
30. 30.What is 96²? =
31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √4624? =
33. 33.A square garden has an area of 3364 square m. How long is each side (in m)?
34. 34.A square garden has an area of 100 square m. How long is each side (in m)?
35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
37. 37.Which of these is a perfect square? (a) 529 (b) 532 (c) 547
38. 38.Which of these is a perfect square? (a) 1369 (b) 1443 (c) 1441
39. 39.What is √7396? =
40. 40.How many whole numbers lie between 43² and 44²?

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