Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 617 · 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 7² and 8²?
2. 2.A square garden has an area of 2500 square m. How long is each side (in m)?
3. 3.What is 12²? =
4. 4.What is √2401? =
5. 5.What is √121? =
6. 6.What is 52²? =
7. 7.A square garden has an area of 2209 square m. How long is each side (in m)?
8. 8.A square garden has an area of 625 square m. How long is each side (in m)?
9. 9.What is the smallest whole number by which 27 must be divided to get a perfect square?
10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 40²? =
12. 12.A square garden has an area of 3136 square m. How long is each side (in m)?
13. 13.What is the smallest whole number by which 128 must be divided to get a perfect square?
14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
15. 15.How many whole numbers lie between 26² and 27²?
16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
17. 17.What is √484? =
18. 18.What is the smallest whole number by which 32 must be divided to get a perfect square?
19. 19.What is √784? =
20. 20.Which of these is a perfect square? (a) 784 (b) 829 (c) 838
21. 21.What is √400? =
22. 22.What is 34²? =
23. 23.How many whole numbers lie between 40² and 41²?
24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 29² and 30²?
26. 26.Which of these is a perfect square? (a) 1156 (b) 1186 (c) 1215
27. 27.What is 23²? =
28. 28.How many whole numbers lie between 34² and 35²?
29. 29.What is √324? =
30. 30.What is 71²? =
31. 31.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
32. 32.What is √5184? =
33. 33.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
34. 34.What is 26²? =
35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 15²? =
37. 37.How many whole numbers lie between 17² and 18²?
38. 38.A square garden has an area of 3481 square m. How long is each side (in m)?
39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
40. 40.Which of these is a perfect square? (a) 100 (b) 104 (c) 119

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