Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 687 · 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.A square garden has an area of 49 square m. How long is each side (in m)?
2. 2.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
3. 3.A square garden has an area of 36 square m. How long is each side (in m)?
4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 32²? =
6. 6.What is √9025? =
7. 7.Which of these is a perfect square? (a) 1532 (b) 1536 (c) 1521
8. 8.Which of these is a perfect square? (a) 400 (b) 440 (c) 417
9. 9.A square garden has an area of 2209 square m. How long is each side (in m)?
10. 10.What is 91²? =
11. 11.A square garden has an area of 2809 square m. How long is each side (in m)?
12. 12.What is 36²? =
13. 13.What is √225? =
14. 14.How many whole numbers lie between 10² and 11²?
15. 15.Which of these is a perfect square? (a) 780 (b) 729 (c) 776
16. 16.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
17. 17.A square garden has an area of 3025 square m. How long is each side (in m)?
18. 18.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
19. 19.What is 16²? =
20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √8464? =
24. 24.What is 12²? =
25. 25.A square garden has an area of 1936 square m. How long is each side (in m)?
26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
27. 27.How many whole numbers lie between 43² and 44²?
28. 28.How many whole numbers lie between 20² and 21²?
29. 29.A square garden has an area of 961 square m. How long is each side (in m)?
30. 30.What is the smallest whole number by which 8 must be divided to get a perfect square?
31. 31.What is √9409? =
32. 32.What is √256? =
33. 33.How many whole numbers lie between 42² and 43²?
34. 34.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √2401? =
38. 38.A square garden has an area of 3249 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 893 (b) 866 (c) 841
40. 40.What is 18²? =

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