Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 39 · 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 √1764? =
2. 2.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
3. 3.What is √4624? =
4. 4.A square garden has an area of 1444 square m. How long is each side (in m)?
5. 5.What is √3969? =
6. 6.What is 71²? =
7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √5184? =
9. 9.What is 37²? =
10. 10.What is 26²? =
11. 11.A square garden has an area of 784 square m. How long is each side (in m)?
12. 12.How many whole numbers lie between 9² and 10²?
13. 13.What is √484? =
14. 14.What is √7056? =
15. 15.What is the smallest whole number by which 45 must be divided to get a perfect square?
16. 16.What is 79²? =
17. 17.What is √3364? =
18. 18.How many whole numbers lie between 6² and 7²?
19. 19.What is 43²? =
20. 20.What is √9801? =
21. 21.What is 54²? =
22. 22.A square garden has an area of 2304 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 38² and 39²?
24. 24.A square garden has an area of 1225 square m. How long is each side (in m)?
25. 25.What is 17²? =
26. 26.Which of these is a perfect square? (a) 925 (b) 936 (c) 900
27. 27.How many whole numbers lie between 37² and 38²?
28. 28.A square garden has an area of 49 square m. How long is each side (in m)?
29. 29.What is 34²? =
30. 30.A square garden has an area of 100 square m. How long is each side (in m)?
31. 31.What is 15²? =
32. 32.What is 83²? =
33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 31² and 32²?
35. 35.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
36. 36.How many whole numbers lie between 12² and 13²?
37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 11² and 12²?
39. 39.Which of these is a perfect square? (a) 1158 (b) 1156 (c) 1206
40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?

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