Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 78 · 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 93²? =
2. 2.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
3. 3.How many whole numbers lie between 14² and 15²?
4. 4.What is 49²? =
5. 5.What is √1681? =
6. 6.What is √289? =
7. 7.A square garden has an area of 484 square m. How long is each side (in m)?
8. 8.What is 31²? =
9. 9.What is √9801? =
10. 10.Which of these is a perfect square? (a) 1596 (b) 1534 (c) 1521
11. 11.A square garden has an area of 2809 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 1024 square m. How long is each side (in m)?
14. 14.A square garden has an area of 361 square m. How long is each side (in m)?
15. 15.What is √3136? =
16. 16.What is 76²? =
17. 17.A square garden has an area of 900 square m. How long is each side (in m)?
18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
19. 19.How many whole numbers lie between 22² and 23²?
20. 20.What is 14²? =
21. 21.What is √4356? =
22. 22.What is 25²? =
23. 23.A square garden has an area of 225 square m. How long is each side (in m)?
24. 24.A square garden has an area of 576 square m. How long is each side (in m)?
25. 25.A square garden has an area of 1600 square m. How long is each side (in m)?
26. 26.A square garden has an area of 3364 square m. How long is each side (in m)?
27. 27.What is 45²? =
28. 28.What is 33²? =
29. 29.What is 43²? =
30. 30.What is √961? =
31. 31.What is 66²? =
32. 32.What is 37²? =
33. 33.Which of these is a perfect square? (a) 889 (b) 897 (c) 841
34. 34.What is the smallest whole number by which 216 must be divided to get a perfect square?
35. 35.Which of these is a perfect square? (a) 808 (b) 795 (c) 784
36. 36.How many whole numbers lie between 30² and 31²?
37. 37.Which of these is a perfect square? (a) 1313 (b) 1304 (c) 1296
38. 38.A square garden has an area of 1156 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 10² and 11²?
40. 40.Which of these is a perfect square? (a) 1086 (b) 1024 (c) 1032

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