Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 638 · 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 the smallest whole number by which 125 must be divided to get a perfect square?
2. 2.What is √5776? =
3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 43²? =
5. 5.How many whole numbers lie between 8² and 9²?
6. 6.A square garden has an area of 81 square m. How long is each side (in m)?
7. 7.What is √2704? =
8. 8.Which of these is a perfect square? (a) 1444 (b) 1482 (c) 1469
9. 9.What is 83²? =
10. 10.A square garden has an area of 3600 square m. How long is each side (in m)?
11. 11.A square garden has an area of 3481 square m. How long is each side (in m)?
12. 12.A square garden has an area of 441 square m. How long is each side (in m)?
13. 13.What is 99²? =
14. 14.How many whole numbers lie between 39² and 40²?
15. 15.What is the smallest whole number by which 126 must be divided to get a perfect square?
16. 16.A square garden has an area of 169 square m. How long is each side (in m)?
17. 17.What is 13²? =
18. 18.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
19. 19.How many whole numbers lie between 17² and 18²?
20. 20.How many whole numbers lie between 49² and 50²?
21. 21.What is 60²? =
22. 22.What is √144? =
23. 23.What is 84²? =
24. 24.A square garden has an area of 2809 square m. How long is each side (in m)?
25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
27. 27.How many whole numbers lie between 38² and 39²?
28. 28.A square garden has an area of 3025 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 12² and 13²?
30. 30.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
31. 31.Which of these is a perfect square? (a) 1281 (b) 1232 (c) 1225
32. 32.What is 41²? =
33. 33.What is 48²? =
34. 34.A square garden has an area of 400 square m. How long is each side (in m)?
35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 59²? =
38. 38.What is the smallest whole number by which 63 must be divided to get a perfect square?
39. 39.A square garden has an area of 2500 square m. How long is each side (in m)?
40. 40.What is √729? =

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