Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 722 · 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 17² and 18²?
2. 2.What is √9604? =
3. 3.How many whole numbers lie between 42² and 43²?
4. 4.Which of these is a perfect square? (a) 660 (b) 625 (c) 664
5. 5.A square garden has an area of 144 square m. How long is each side (in m)?
6. 6.How many whole numbers lie between 25² and 26²?
7. 7.Which of these is a perfect square? (a) 624 (b) 576 (c) 586
8. 8.Which of these is a perfect square? (a) 1206 (b) 1186 (c) 1156
9. 9.Which of these is a perfect square? (a) 441 (b) 474 (c) 452
10. 10.What is 68²? =
11. 11.What is √8836? =
12. 12.What is √4096? =
13. 13.A square garden has an area of 841 square m. How long is each side (in m)?
14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √676? =
16. 16.How many whole numbers lie between 46² and 47²?
17. 17.A square garden has an area of 100 square m. How long is each side (in m)?
18. 18.What is the smallest whole number by which 20 must be divided to get a perfect square?
19. 19.What is 35²? =
20. 20.What is the smallest whole number by which 1134 must be divided to get a perfect square?
21. 21.A square garden has an area of 1089 square m. How long is each side (in m)?
22. 22.What is the smallest whole number by which 128 must be divided to get a perfect square?
23. 23.How many whole numbers lie between 18² and 19²?
24. 24.What is 38²? =
25. 25.A square garden has an area of 1600 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
27. 27.What is √2025? =
28. 28.How many whole numbers lie between 34² and 35²?
29. 29.Which of these is a perfect square? (a) 177 (b) 180 (c) 169
30. 30.What is the smallest whole number by which 384 must be divided to get a perfect square?
31. 31.What is 58²? =
32. 32.How many whole numbers lie between 7² and 8²?
33. 33.How many whole numbers lie between 5² and 6²?
34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 19² and 20²?
36. 36.A square garden has an area of 961 square m. How long is each side (in m)?
37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √5041? =
39. 39.What is √1296? =
40. 40.What is the smallest whole number by which 20 must be multiplied to get a perfect square?

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