Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 307 · 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 √144? =
2. 2.What is the smallest whole number by which 98 must be divided to get a perfect square?
3. 3.What is 16²? =
4. 4.What is √1024? =
5. 5.A square garden has an area of 900 square m. How long is each side (in m)?
6. 6.A square garden has an area of 64 square m. How long is each side (in m)?
7. 7.Which of these is a perfect square? (a) 789 (b) 784 (c) 825
8. 8.Which of these is a perfect square? (a) 985 (b) 961 (c) 964
9. 9.Which of these is a perfect square? (a) 777 (b) 729 (c) 780
10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 1215 must be divided to get a perfect square?
12. 12.A square garden has an area of 324 square m. How long is each side (in m)?
13. 13.A square garden has an area of 1936 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 12² and 13²?
15. 15.What is √9409? =
16. 16.What is √3249? =
17. 17.What is 31²? =
18. 18.What is 30²? =
19. 19.How many whole numbers lie between 38² and 39²?
20. 20.What is √1369? =
21. 21.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
22. 22.What is √6561? =
23. 23.A square garden has an area of 2500 square m. How long is each side (in m)?
24. 24.What is 66²? =
25. 25.How many whole numbers lie between 48² and 49²?
26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
28. 28.What is 64²? =
29. 29.Which of these is a perfect square? (a) 1566 (b) 1551 (c) 1521
30. 30.What is √361? =
31. 31.How many whole numbers lie between 22² and 23²?
32. 32.A square garden has an area of 3481 square m. How long is each side (in m)?
33. 33.What is 49²? =
34. 34.A square garden has an area of 121 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 1650 (b) 1600 (c) 1623
36. 36.A square garden has an area of 2304 square m. How long is each side (in m)?
37. 37.What is 25²? =
38. 38.What is 27²? =
39. 39.How many whole numbers lie between 39² and 40²?
40. 40.How many whole numbers lie between 11² and 12²?

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