Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 245 · 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.What is 49²? =
2. 2.A square garden has an area of 196 square m. How long is each side (in m)?
3. 3.What is √484? =
4. 4.Which of these is a perfect square? (a) 882 (b) 841 (c) 848
5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the smallest whole number by which 810 must be divided to get a perfect square?
7. 7.A square garden has an area of 25 square m. How long is each side (in m)?
8. 8.What is √256? =
9. 9.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
10. 10.What is 33²? =
11. 11.What is 75²? =
12. 12.What is 17²? =
13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
14. 14.Which of these is a perfect square? (a) 121 (b) 122 (c) 142
15. 15.What is 83²? =
16. 16.A square garden has an area of 3481 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 32² and 33²?
18. 18.A square garden has an area of 1521 square m. How long is each side (in m)?
19. 19.What is √841? =
20. 20.How many whole numbers lie between 45² and 46²?
21. 21.What is the smallest whole number by which 48 must be divided to get a perfect square?
22. 22.A square garden has an area of 900 square m. How long is each side (in m)?
23. 23.A square garden has an area of 289 square m. How long is each side (in m)?
24. 24.What is √6241? =
25. 25.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the smallest whole number by which 192 must be divided to get a perfect square?
28. 28.Which of these is a perfect square? (a) 1097 (b) 1099 (c) 1089
29. 29.A square garden has an area of 49 square m. How long is each side (in m)?
30. 30.What is √625? =
31. 31.What is the smallest whole number by which 54 must be divided to get a perfect square?
32. 32.What is 73²? =
33. 33.What is 62²? =
34. 34.How many whole numbers lie between 41² and 42²?
35. 35.What is 90²? =
36. 36.How many whole numbers lie between 33² and 34²?
37. 37.A square garden has an area of 3364 square m. How long is each side (in m)?
38. 38.What is √9409? =
39. 39.Which of these is a perfect square? (a) 112 (b) 100 (c) 101
40. 40.What is the smallest whole number by which 27 must be multiplied to get a perfect square?

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