Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 390 · 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 √8464? =
2. 2.Which of these is a perfect square? (a) 702 (b) 687 (c) 676
3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √8281? =
5. 5.What is the smallest whole number by which 176 must be divided to get a perfect square?
6. 6.A square garden has an area of 3136 square m. How long is each side (in m)?
7. 7.Which of these is a perfect square? (a) 966 (b) 978 (c) 961
8. 8.What is the smallest whole number by which 539 must be divided to get a perfect square?
9. 9.What is 46²? =
10. 10.What is √1369? =
11. 11.Which of these is a perfect square? (a) 484 (b) 511 (c) 497
12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 19² and 20²?
14. 14.What is √5329? =
15. 15.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
16. 16.How many whole numbers lie between 47² and 48²?
17. 17.What is √5184? =
18. 18.A square garden has an area of 1849 square m. How long is each side (in m)?
19. 19.What is √1444? =
20. 20.What is 61²? =
21. 21.What is √2916? =
22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 7² and 8²?
26. 26.What is 82²? =
27. 27.What is √1296? =
28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 1296 (b) 1322 (c) 1321
30. 30.A square garden has an area of 196 square m. How long is each side (in m)?
31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √1681? =
33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 16² and 17²?
35. 35.What is √4761? =
36. 36.How many whole numbers lie between 24² and 25²?
37. 37.A square garden has an area of 625 square m. How long is each side (in m)?
38. 38.What is √8100? =
39. 39.A square garden has an area of 25 square m. How long is each side (in m)?
40. 40.What is the smallest whole number by which 896 must be divided to get a perfect square?

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