Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 43 · 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 729 square m. How long is each side (in m)?
2. 2.What is 83²? =
3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 80²? =
5. 5.Which of these is a perfect square? (a) 403 (b) 417 (c) 400
6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √576? =
8. 8.Which of these is a perfect square? (a) 1265 (b) 1234 (c) 1225
9. 9.What is 98²? =
10. 10.What is the smallest whole number by which 245 must be divided to get a perfect square?
11. 11.What is 29²? =
12. 12.What is √441? =
13. 13.What is the smallest whole number by which 250 must be divided to get a perfect square?
14. 14.How many whole numbers lie between 6² and 7²?
15. 15.How many whole numbers lie between 18² and 19²?
16. 16.What is 87²? =
17. 17.What is 86²? =
18. 18.How many whole numbers lie between 39² and 40²?
19. 19.A square garden has an area of 3249 square m. How long is each side (in m)?
20. 20.What is 35²? =
21. 21.How many whole numbers lie between 16² and 17²?
22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √8464? =
24. 24.How many whole numbers lie between 25² and 26²?
25. 25.How many whole numbers lie between 48² and 49²?
26. 26.What is √1600? =
27. 27.What is 51²? =
28. 28.What is 57²? =
29. 29.What is 49²? =
30. 30.What is 31²? =
31. 31.How many whole numbers lie between 17² and 18²?
32. 32.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
34. 34.Which of these is a perfect square? (a) 1082 (b) 1059 (c) 1024
35. 35.What is the smallest whole number by which 468 must be divided to get a perfect square?
36. 36.A square garden has an area of 225 square m. How long is each side (in m)?
37. 37.What is 22²? =
38. 38.How many whole numbers lie between 45² and 46²?
39. 39.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
40. 40.How many whole numbers lie between 5² and 6²?

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