Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 17 · 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 25 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 99²? =
3. 3.How many whole numbers lie between 6² and 7²?
4. 4.What is 29²? =
5. 5.How many whole numbers lie between 29² and 30²?
6. 6.What is √7744? =
7. 7.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
8. 8.What is √2304? =
9. 9.Which of these is a perfect square? (a) 355 (b) 324 (c) 343
10. 10.Which of these is a perfect square? (a) 729 (b) 759 (c) 752
11. 11.What is √529? =
12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 49² and 50²?
14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 67²? =
16. 16.Which of these is a perfect square? (a) 1169 (b) 1156 (c) 1176
17. 17.What is the smallest whole number by which 54 must be divided to get a perfect square?
18. 18.Which of these is a perfect square? (a) 961 (b) 1016 (c) 962
19. 19.What is √1681? =
20. 20.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 144 (b) 168 (c) 157
22. 22.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
24. 24.How many whole numbers lie between 15² and 16²?
25. 25.What is √784? =
26. 26.A square garden has an area of 144 square m. How long is each side (in m)?
27. 27.What is 22²? =
28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the smallest whole number by which 240 must be divided to get a perfect square?
31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
33. 33.A square garden has an area of 3364 square m. How long is each side (in m)?
34. 34.How many whole numbers lie between 17² and 18²?
35. 35.What is 92²? =
36. 36.What is 71²? =
37. 37.What is the smallest whole number by which 135 must be divided to get a perfect square?
38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
39. 39.A square garden has an area of 1444 square m. How long is each side (in m)?
40. 40.What is the smallest whole number by which 896 must be divided to get a perfect square?

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