Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 672 · 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 36 square m. How long is each side (in m)?
2. 2.What is √784? =
3. 3.What is √9409? =
4. 4.What is √361? =
5. 5.How many whole numbers lie between 25² and 26²?
6. 6.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
7. 7.What is the smallest whole number by which 40 must be divided to get a perfect square?
8. 8.What is √4356? =
9. 9.A square garden has an area of 49 square m. How long is each side (in m)?
10. 10.A square garden has an area of 841 square m. How long is each side (in m)?
11. 11.What is √324? =
12. 12.What is 51²? =
13. 13.What is 45²? =
14. 14.What is the smallest whole number by which 224 must be divided to get a perfect square?
15. 15.A square garden has an area of 1521 square m. How long is each side (in m)?
16. 16.A square garden has an area of 1600 square m. How long is each side (in m)?
17. 17.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √8649? =
20. 20.Which of these is a perfect square? (a) 305 (b) 319 (c) 289
21. 21.What is the smallest whole number by which 27 must be divided to get a perfect square?
22. 22.A square garden has an area of 1444 square m. How long is each side (in m)?
23. 23.What is 89²? =
24. 24.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
25. 25.What is √441? =
26. 26.How many whole numbers lie between 42² and 43²?
27. 27.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
28. 28.How many whole numbers lie between 34² and 35²?
29. 29.How many whole numbers lie between 15² and 16²?
30. 30.How many whole numbers lie between 41² and 42²?
31. 31.How many whole numbers lie between 30² and 31²?
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √2401? =
34. 34.What is 44²? =
35. 35.What is √6561? =
36. 36.A square garden has an area of 81 square m. How long is each side (in m)?
37. 37.What is 36²? =
38. 38.Which of these is a perfect square? (a) 121 (b) 128 (c) 127
39. 39.A square garden has an area of 1681 square m. How long is each side (in m)?
40. 40.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?

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