Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 238 · 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.How many whole numbers lie between 5² and 6²?
2. 2.What is √8100? =
3. 3.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
4. 4.What is √1024? =
5. 5.How many whole numbers lie between 18² and 19²?
6. 6.A square garden has an area of 961 square m. How long is each side (in m)?
7. 7.What is 23²? =
8. 8.What is 65²? =
9. 9.Which of these is a perfect square? (a) 1156 (b) 1175 (c) 1187
10. 10.A square garden has an area of 400 square m. How long is each side (in m)?
11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 61²? =
13. 13.How many whole numbers lie between 48² and 49²?
14. 14.Which of these is a perfect square? (a) 866 (b) 841 (c) 856
15. 15.What is √1225? =
16. 16.A square garden has an area of 64 square m. How long is each side (in m)?
17. 17.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
18. 18.What is 17²? =
19. 19.What is the smallest whole number by which 320 must be divided to get a perfect square?
20. 20.What is 36²? =
21. 21.What is 68²? =
22. 22.How many whole numbers lie between 15² and 16²?
23. 23.What is √676? =
24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √576? =
26. 26.What is 62²? =
27. 27.What is the smallest whole number by which 32 must be divided to get a perfect square?
28. 28.A square garden has an area of 3481 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 28² and 29²?
30. 30.What is 67²? =
31. 31.What is 75²? =
32. 32.What is 39²? =
33. 33.What is the smallest whole number by which 192 must be divided to get a perfect square?
34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
35. 35.Which of these is a perfect square? (a) 250 (b) 225 (c) 247
36. 36.What is √625? =
37. 37.Which of these is a perfect square? (a) 808 (b) 784 (c) 826
38. 38.What is 76²? =
39. 39.A square garden has an area of 1600 square m. How long is each side (in m)?
40. 40.What is √5329? =

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