Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 536 · 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 √3249? =
2. 2.What is 49²? =
3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 241 (b) 225 (c) 248
5. 5.What is 83²? =
6. 6.How many whole numbers lie between 48² and 49²?
7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 30²? =
9. 9.How many whole numbers lie between 9² and 10²?
10. 10.How many whole numbers lie between 7² and 8²?
11. 11.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
13. 13.What is √400? =
14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
15. 15.How many whole numbers lie between 39² and 40²?
16. 16.A square garden has an area of 64 square m. How long is each side (in m)?
17. 17.What is 54²? =
18. 18.What is √2025? =
19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √1849? =
21. 21.What is 55²? =
22. 22.A square garden has an area of 1764 square m. How long is each side (in m)?
23. 23.What is √4624? =
24. 24.What is √1089? =
25. 25.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √576? =
28. 28.What is 69²? =
29. 29.What is 23²? =
30. 30.Which of these is a perfect square? (a) 186 (b) 179 (c) 169
31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
32. 32.A square garden has an area of 1444 square m. How long is each side (in m)?
33. 33.What is 80²? =
34. 34.A square garden has an area of 256 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 6² and 7²?
36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
37. 37.How many whole numbers lie between 47² and 48²?
38. 38.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
39. 39.What is √324? =
40. 40.What is the smallest whole number by which 486 must be multiplied to get a perfect square?

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