Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 503 · 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) 1133 (b) 1134 (c) 1089
2. 2.What is 65²? =
3. 3.A square garden has an area of 25 square m. How long is each side (in m)?
4. 4.What is 44²? =
5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 93²? =
7. 7.Which of these is a perfect square? (a) 1626 (b) 1600 (c) 1619
8. 8.What is 74²? =
9. 9.What is the smallest whole number by which 1215 must be divided to get a perfect square?
10. 10.What is √169? =
11. 11.A square garden has an area of 100 square m. How long is each side (in m)?
12. 12.What is 53²? =
13. 13.Which of these is a perfect square? (a) 784 (b) 814 (c) 807
14. 14.What is √6084? =
15. 15.How many whole numbers lie between 45² and 46²?
16. 16.A square garden has an area of 1156 square m. How long is each side (in m)?
17. 17.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 1225 (b) 1266 (c) 1248
20. 20.A square garden has an area of 361 square m. How long is each side (in m)?
21. 21.What is 38²? =
22. 22.How many whole numbers lie between 47² and 48²?
23. 23.What is 18²? =
24. 24.A square garden has an area of 144 square m. How long is each side (in m)?
25. 25.Which of these is a perfect square? (a) 1024 (b) 1068 (c) 1026
26. 26.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √1849? =
28. 28.A square garden has an area of 900 square m. How long is each side (in m)?
29. 29.What is √625? =
30. 30.What is 30²? =
31. 31.Which of these is a perfect square? (a) 724 (b) 699 (c) 676
32. 32.A square garden has an area of 2704 square m. How long is each side (in m)?
33. 33.A square garden has an area of 400 square m. How long is each side (in m)?
34. 34.A square garden has an area of 961 square m. How long is each side (in m)?
35. 35.What is 11²? =
36. 36.A square garden has an area of 1225 square m. How long is each side (in m)?
37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
38. 38.Which of these is a perfect square? (a) 279 (b) 280 (c) 256
39. 39.What is √4624? =
40. 40.What is the smallest whole number by which 60 must be multiplied to get a perfect square?

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