Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 599 · 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) 114 (b) 112 (c) 100
2. 2.What is 78²? =
3. 3.What is √676? =
4. 4.How many whole numbers lie between 22² and 23²?
5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √961? =
7. 7.How many whole numbers lie between 47² and 48²?
8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
9. 9.A square garden has an area of 841 square m. How long is each side (in m)?
10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
13. 13.What is √441? =
14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 88²? =
16. 16.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
17. 17.What is 87²? =
18. 18.A square garden has an area of 1296 square m. How long is each side (in m)?
19. 19.What is √9801? =
20. 20.How many whole numbers lie between 30² and 31²?
21. 21.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
23. 23.How many whole numbers lie between 34² and 35²?
24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √256? =
26. 26.What is √1521? =
27. 27.What is √1764? =
28. 28.What is 94²? =
29. 29.What is 58²? =
30. 30.A square garden has an area of 2500 square m. How long is each side (in m)?
31. 31.What is √784? =
32. 32.Which of these is a perfect square? (a) 218 (b) 211 (c) 196
33. 33.A square garden has an area of 289 square m. How long is each side (in m)?
34. 34.What is √8649? =
35. 35.What is 57²? =
36. 36.How many whole numbers lie between 31² and 32²?
37. 37.What is 13²? =
38. 38.What is √841? =
39. 39.What is 36²? =
40. 40.What is √6561? =

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