Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 548 · 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 √6400? =
2. 2.What is 76²? =
3. 3.Which of these is a perfect square? (a) 1521 (b) 1535 (c) 1573
4. 4.How many whole numbers lie between 36² and 37²?
5. 5.What is 43²? =
6. 6.How many whole numbers lie between 42² and 43²?
7. 7.What is √9025? =
8. 8.What is 69²? =
9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
10. 10.Which of these is a perfect square? (a) 1435 (b) 1428 (c) 1369
11. 11.What is √900? =
12. 12.What is 51²? =
13. 13.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
14. 14.What is the smallest whole number by which 175 must be divided to get a perfect square?
15. 15.What is the smallest whole number by which 48 must be divided to get a perfect square?
16. 16.How many whole numbers lie between 20² and 21²?
17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
18. 18.What is 21²? =
19. 19.What is 13²? =
20. 20.Which of these is a perfect square? (a) 1008 (b) 961 (c) 992
21. 21.A square garden has an area of 1156 square m. How long is each side (in m)?
22. 22.Which of these is a perfect square? (a) 1101 (b) 1089 (c) 1135
23. 23.How many whole numbers lie between 45² and 46²?
24. 24.How many whole numbers lie between 28² and 29²?
25. 25.What is 28²? =
26. 26.What is √1764? =
27. 27.What is the smallest whole number by which 96 must be divided to get a perfect square?
28. 28.What is 42²? =
29. 29.A square garden has an area of 2809 square m. How long is each side (in m)?
30. 30.What is √1444? =
31. 31.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
32. 32.How many whole numbers lie between 9² and 10²?
33. 33.What is √1296? =
34. 34.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
35. 35.What is √5625? =
36. 36.What is the smallest whole number by which 252 must be divided to get a perfect square?
37. 37.What is √289? =
38. 38.A square garden has an area of 625 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 34² and 35²?
40. 40.Which of these is a perfect square? (a) 771 (b) 766 (c) 729

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