Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 415 · 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 31² and 32²?
2. 2.Which of these is a perfect square? (a) 115 (b) 108 (c) 100
3. 3.What is 28²? =
4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 11² and 12²?
6. 6.Which of these is a perfect square? (a) 784 (b) 796 (c) 826
7. 7.What is √4489? =
8. 8.What is the smallest whole number by which 637 must be divided to get a perfect square?
9. 9.What is 15²? =
10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 151 (b) 144 (c) 161
12. 12.What is √3025? =
13. 13.What is 57²? =
14. 14.What is √2916? =
15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
16. 16.A square garden has an area of 625 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 9² and 10²?
18. 18.What is the smallest whole number by which 1215 must be divided to get a perfect square?
19. 19.How many whole numbers lie between 14² and 15²?
20. 20.A square garden has an area of 484 square m. How long is each side (in m)?
21. 21.What is 89²? =
22. 22.A square garden has an area of 196 square m. How long is each side (in m)?
23. 23.What is √2304? =
24. 24.Which of these is a perfect square? (a) 367 (b) 398 (c) 361
25. 25.A square garden has an area of 25 square m. How long is each side (in m)?
26. 26.What is √4225? =
27. 27.What is 76²? =
28. 28.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 1246 (b) 1265 (c) 1225
30. 30.What is 49²? =
31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 933 (b) 907 (c) 900
33. 33.Which of these is a perfect square? (a) 769 (b) 729 (c) 732
34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 50² and 51²?
36. 36.A square garden has an area of 169 square m. How long is each side (in m)?
37. 37.What is 35²? =
38. 38.How many whole numbers lie between 7² and 8²?
39. 39.What is √7744? =
40. 40.What is the smallest whole number by which 48 must be divided to get a perfect square?

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