Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 721 · 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 48²? =
2. 2.What is √3844? =
3. 3.What is 21²? =
4. 4.What is 81²? =
5. 5.What is 18²? =
6. 6.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
7. 7.How many whole numbers lie between 46² and 47²?
8. 8.What is 79²? =
9. 9.How many whole numbers lie between 34² and 35²?
10. 10.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
11. 11.How many whole numbers lie between 8² and 9²?
12. 12.What is √5625? =
13. 13.A square garden has an area of 81 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 169 (b) 172 (c) 181
15. 15.What is 43²? =
16. 16.What is √8649? =
17. 17.A square garden has an area of 2304 square m. How long is each side (in m)?
18. 18.A square garden has an area of 49 square m. How long is each side (in m)?
19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the smallest whole number by which 960 must be divided to get a perfect square?
21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
23. 23.What is 50²? =
24. 24.What is the smallest whole number by which 162 must be divided to get a perfect square?
25. 25.A square garden has an area of 100 square m. How long is each side (in m)?
26. 26.What is √1369? =
27. 27.What is 15²? =
28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 71²? =
30. 30.A square garden has an area of 36 square m. How long is each side (in m)?
31. 31.What is √1936? =
32. 32.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
33. 33.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
34. 34.Which of these is a perfect square? (a) 1024 (b) 1049 (c) 1068
35. 35.What is √961? =
36. 36.What is 42²? =
37. 37.What is √9409? =
38. 38.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
39. 39.What is √576? =
40. 40.What is 68²? =

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