Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 682 · 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 the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 2809 square m. How long is each side (in m)?
3. 3.How many whole numbers lie between 32² and 33²?
4. 4.What is √729? =
5. 5.A square garden has an area of 361 square m. How long is each side (in m)?
6. 6.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
7. 7.What is √196? =
8. 8.What is 73²? =
9. 9.What is 24²? =
10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 1521 square m. How long is each side (in m)?
12. 12.Which of these is a perfect square? (a) 1174 (b) 1178 (c) 1156
13. 13.What is √3249? =
14. 14.Which of these is a perfect square? (a) 482 (b) 441 (c) 478
15. 15.How many whole numbers lie between 22² and 23²?
16. 16.What is 44²? =
17. 17.What is 16²? =
18. 18.A square garden has an area of 841 square m. How long is each side (in m)?
19. 19.What is √1936? =
20. 20.What is √900? =
21. 21.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
22. 22.How many whole numbers lie between 46² and 47²?
23. 23.What is 23²? =
24. 24.How many whole numbers lie between 12² and 13²?
25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
26. 26.What is √1849? =
27. 27.What is √9801? =
28. 28.A square garden has an area of 1296 square m. How long is each side (in m)?
29. 29.What is √4096? =
30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
31. 31.How many whole numbers lie between 38² and 39²?
32. 32.What is 72²? =
33. 33.What is 47²? =
34. 34.A square garden has an area of 1156 square m. How long is each side (in m)?
35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 65²? =
37. 37.How many whole numbers lie between 15² and 16²?
38. 38.What is 75²? =
39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
40. 40.Which of these is a perfect square? (a) 429 (b) 400 (c) 438

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