Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 540 · 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 √1156? =
2. 2.What is √196? =
3. 3.What is 93²? =
4. 4.What is √289? =
5. 5.Which of these is a perfect square? (a) 196 (b) 205 (c) 204
6. 6.What is √1089? =
7. 7.What is 50²? =
8. 8.What is √3481? =
9. 9.What is 92²? =
10. 10.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
11. 11.What is 77²? =
12. 12.What is 14²? =
13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the smallest whole number by which 52 must be divided to get a perfect square?
15. 15.What is 24²? =
16. 16.How many whole numbers lie between 8² and 9²?
17. 17.How many whole numbers lie between 10² and 11²?
18. 18.What is 21²? =
19. 19.What is 23²? =
20. 20.What is 51²? =
21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 75²? =
23. 23.What is √4096? =
24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 20² and 21²?
26. 26.A square garden has an area of 196 square m. How long is each side (in m)?
27. 27.Which of these is a perfect square? (a) 732 (b) 742 (c) 729
28. 28.A square garden has an area of 1024 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 144 (b) 160 (c) 146
30. 30.How many whole numbers lie between 34² and 35²?
31. 31.What is √5625? =
32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
35. 35.What is √7921? =
36. 36.Which of these is a perfect square? (a) 900 (b) 930 (c) 927
37. 37.A square garden has an area of 400 square m. How long is each side (in m)?
38. 38.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
39. 39.How many whole numbers lie between 19² and 20²?
40. 40.What is 44²? =

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