Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 733 · 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.Which of these is a perfect square? (a) 256 (b) 286 (c) 282
2. 2.What is 26²? =
3. 3.A square garden has an area of 81 square m. How long is each side (in m)?
4. 4.What is √441? =
5. 5.A square garden has an area of 841 square m. How long is each side (in m)?
6. 6.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
8. 8.A square garden has an area of 361 square m. How long is each side (in m)?
9. 9.A square garden has an area of 2916 square m. How long is each side (in m)?
10. 10.What is 49²? =
11. 11.How many whole numbers lie between 20² and 21²?
12. 12.What is √1849? =
13. 13.How many whole numbers lie between 15² and 16²?
14. 14.What is √4624? =
15. 15.What is √4900? =
16. 16.How many whole numbers lie between 30² and 31²?
17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 18² and 19²?
19. 19.What is √484? =
20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
21. 21.Which of these is a perfect square? (a) 1233 (b) 1264 (c) 1225
22. 22.What is √6241? =
23. 23.What is √225? =
24. 24.Which of these is a perfect square? (a) 1156 (b) 1212 (c) 1170
25. 25.What is 41²? =
26. 26.What is 44²? =
27. 27.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
28. 28.A square garden has an area of 196 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 50 must be divided to get a perfect square?
30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
32. 32.What is √3721? =
33. 33.What is 53²? =
34. 34.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 85²? =
36. 36.A square garden has an area of 1764 square m. How long is each side (in m)?
37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √5929? =
39. 39.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
40. 40.A square garden has an area of 64 square m. How long is each side (in m)?

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