Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 107 · 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 28² and 29²?
2. 2.What is 66²? =
3. 3.What is √9604? =
4. 4.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
5. 5.What is 72²? =
6. 6.Which of these is a perfect square? (a) 1296 (b) 1328 (c) 1332
7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
8. 8.A square garden has an area of 1681 square m. How long is each side (in m)?
9. 9.What is √6241? =
10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √7225? =
12. 12.A square garden has an area of 1849 square m. How long is each side (in m)?
13. 13.What is 68²? =
14. 14.A square garden has an area of 676 square m. How long is each side (in m)?
15. 15.What is the smallest whole number by which 350 must be divided to get a perfect square?
16. 16.What is the smallest whole number by which 208 must be divided to get a perfect square?
17. 17.What is 58²? =
18. 18.What is 86²? =
19. 19.What is √169? =
20. 20.What is √4900? =
21. 21.How many whole numbers lie between 20² and 21²?
22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 18²? =
24. 24.Which of these is a perfect square? (a) 1050 (b) 1024 (c) 1054
25. 25.Which of these is a perfect square? (a) 185 (b) 187 (c) 169
26. 26.Which of these is a perfect square? (a) 905 (b) 903 (c) 900
27. 27.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
28. 28.What is √1296? =
29. 29.How many whole numbers lie between 15² and 16²?
30. 30.A square garden has an area of 441 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 829 (b) 793 (c) 784
32. 32.Which of these is a perfect square? (a) 1103 (b) 1098 (c) 1089
33. 33.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
34. 34.What is √289? =
35. 35.What is √4356? =
36. 36.What is √625? =
37. 37.How many whole numbers lie between 45² and 46²?
38. 38.What is the smallest whole number by which 150 must be divided to get a perfect square?
39. 39.What is √5476? =
40. 40.How many whole numbers lie between 6² and 7²?

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