Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 338 · 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 60²? =
2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 65²? =
4. 4.A square garden has an area of 1296 square m. How long is each side (in m)?
5. 5.What is √784? =
6. 6.How many whole numbers lie between 39² and 40²?
7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 19²? =
9. 9.What is √1296? =
10. 10.Which of these is a perfect square? (a) 304 (b) 289 (c) 306
11. 11.What is √7396? =
12. 12.What is √900? =
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
14. 14.A square garden has an area of 361 square m. How long is each side (in m)?
15. 15.What is √484? =
16. 16.How many whole numbers lie between 30² and 31²?
17. 17.A square garden has an area of 400 square m. How long is each side (in m)?
18. 18.What is the smallest whole number by which 294 must be divided to get a perfect square?
19. 19.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
20. 20.Which of these is a perfect square? (a) 953 (b) 914 (c) 900
21. 21.Which of these is a perfect square? (a) 251 (b) 225 (c) 226
22. 22.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
23. 23.What is 96²? =
24. 24.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
25. 25.What is √6889? =
26. 26.What is 46²? =
27. 27.What is 86²? =
28. 28.What is 59²? =
29. 29.A square garden has an area of 2116 square m. How long is each side (in m)?
30. 30.A square garden has an area of 2401 square m. How long is each side (in m)?
31. 31.What is √3481? =
32. 32.A square garden has an area of 49 square m. How long is each side (in m)?
33. 33.What is 85²? =
34. 34.What is √7569? =
35. 35.What is 61²? =
36. 36.Which of these is a perfect square? (a) 360 (b) 324 (c) 330
37. 37.How many whole numbers lie between 12² and 13²?
38. 38.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
39. 39.What is the smallest whole number by which 117 must be divided to get a perfect square?
40. 40.What is √3600? =

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