Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 3 · 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 the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
2. 2.What is √1369? =
3. 3.What is the smallest whole number by which 72 must be divided to get a perfect square?
4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 45²? =
6. 6.What is 28²? =
7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 41²? =
9. 9.Which of these is a perfect square? (a) 1444 (b) 1480 (c) 1496
10. 10.What is 55²? =
11. 11.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 49² and 50²?
14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 22²? =
16. 16.What is 24²? =
17. 17.What is 67²? =
18. 18.A square garden has an area of 2916 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 90 must be divided to get a perfect square?
20. 20.How many whole numbers lie between 34² and 35²?
21. 21.What is √5776? =
22. 22.A square garden has an area of 1600 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 23² and 24²?
24. 24.What is √8464? =
25. 25.What is 51²? =
26. 26.How many whole numbers lie between 21² and 22²?
27. 27.What is 79²? =
28. 28.How many whole numbers lie between 10² and 11²?
29. 29.What is 29²? =
30. 30.A square garden has an area of 1764 square m. How long is each side (in m)?
31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 841 (b) 875 (c) 896
33. 33.What is the smallest whole number by which 128 must be divided to get a perfect square?
34. 34.What is √784? =
35. 35.A square garden has an area of 729 square m. How long is each side (in m)?
36. 36.Which of these is a perfect square? (a) 1427 (b) 1369 (c) 1387
37. 37.What is √9025? =
38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √6889? =
40. 40.How many whole numbers lie between 45² and 46²?

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