Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 492 · 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 22 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 84²? =
3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 117 (b) 100 (c) 112
5. 5.How many whole numbers lie between 44² and 45²?
6. 6.What is √3600? =
7. 7.What is 58²? =
8. 8.What is the smallest whole number by which 150 must be divided to get a perfect square?
9. 9.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
10. 10.A square garden has an area of 484 square m. How long is each side (in m)?
11. 11.A square garden has an area of 2809 square m. How long is each side (in m)?
12. 12.How many whole numbers lie between 7² and 8²?
13. 13.How many whole numbers lie between 50² and 51²?
14. 14.How many whole numbers lie between 22² and 23²?
15. 15.How many whole numbers lie between 24² and 25²?
16. 16.What is √6889? =
17. 17.What is 59²? =
18. 18.Which of these is a perfect square? (a) 137 (b) 121 (c) 126
19. 19.A square garden has an area of 324 square m. How long is each side (in m)?
20. 20.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
21. 21.What is √3249? =
22. 22.A square garden has an area of 121 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 39² and 40²?
24. 24.What is 92²? =
25. 25.What is 97²? =
26. 26.What is √289? =
27. 27.What is 12²? =
28. 28.Which of these is a perfect square? (a) 1147 (b) 1089 (c) 1094
29. 29.A square garden has an area of 81 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 9² and 10²?
31. 31.How many whole numbers lie between 32² and 33²?
32. 32.Which of these is a perfect square? (a) 972 (b) 1006 (c) 961
33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 12² and 13²?
35. 35.What is √1849? =
36. 36.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
37. 37.A square garden has an area of 361 square m. How long is each side (in m)?
38. 38.What is 90²? =
39. 39.What is 91²? =
40. 40.How many whole numbers lie between 14² and 15²?

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