Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 374 · 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 361 square m. How long is each side (in m)?
2. 2.How many whole numbers lie between 45² and 46²?
3. 3.What is the smallest whole number by which 686 must be divided to get a perfect square?
4. 4.What is √225? =
5. 5.What is √5476? =
6. 6.A square garden has an area of 1936 square m. How long is each side (in m)?
7. 7.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 24²? =
10. 10.Which of these is a perfect square? (a) 100 (b) 116 (c) 111
11. 11.What is √7744? =
12. 12.A square garden has an area of 100 square m. How long is each side (in m)?
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 66²? =
15. 15.What is 56²? =
16. 16.A square garden has an area of 121 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 900 (b) 938 (c) 902
18. 18.What is √400? =
19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
20. 20.How many whole numbers lie between 11² and 12²?
21. 21.Which of these is a perfect square? (a) 441 (b) 447 (c) 468
22. 22.Which of these is a perfect square? (a) 144 (b) 145 (c) 153
23. 23.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
24. 24.What is the smallest whole number by which 135 must be divided to get a perfect square?
25. 25.What is 76²? =
26. 26.How many whole numbers lie between 12² and 13²?
27. 27.What is √729? =
28. 28.What is √529? =
29. 29.What is 36²? =
30. 30.What is √6400? =
31. 31.Which of these is a perfect square? (a) 121 (b) 141 (c) 133
32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
34. 34.Which of these is a perfect square? (a) 400 (b) 433 (c) 410
35. 35.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
36. 36.What is 93²? =
37. 37.What is the smallest whole number by which 99 must be divided to get a perfect square?
38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 48²? =
40. 40.A square garden has an area of 2401 square m. How long is each side (in m)?

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