Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 54 · 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 32²? =
2. 2.How many whole numbers lie between 31² and 32²?
3. 3.Which of these is a perfect square? (a) 634 (b) 666 (c) 625
4. 4.What is 40²? =
5. 5.Which of these is a perfect square? (a) 112 (b) 100 (c) 119
6. 6.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
7. 7.A square garden has an area of 2809 square m. How long is each side (in m)?
8. 8.What is 14²? =
9. 9.What is the smallest whole number by which 98 must be divided to get a perfect square?
10. 10.Which of these is a perfect square? (a) 1368 (b) 1296 (c) 1345
11. 11.What is √196? =
12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 280 (b) 256 (c) 288
14. 14.What is 67²? =
15. 15.What is 84²? =
16. 16.What is √961? =
17. 17.Which of these is a perfect square? (a) 816 (b) 784 (c) 786
18. 18.What is the smallest whole number by which 162 must be divided to get a perfect square?
19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
21. 21.How many whole numbers lie between 5² and 6²?
22. 22.What is 95²? =
23. 23.What is √5041? =
24. 24.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
25. 25.A square garden has an area of 36 square m. How long is each side (in m)?
26. 26.How many whole numbers lie between 11² and 12²?
27. 27.A square garden has an area of 1024 square m. How long is each side (in m)?
28. 28.What is 56²? =
29. 29.What is 51²? =
30. 30.A square garden has an area of 1849 square m. How long is each side (in m)?
31. 31.What is √3481? =
32. 32.How many whole numbers lie between 20² and 21²?
33. 33.What is the smallest whole number by which 240 must be divided to get a perfect square?
34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 55²? =
36. 36.What is 66²? =
37. 37.What is the smallest whole number by which 224 must be divided to get a perfect square?
38. 38.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
40. 40.What is 70²? =

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