Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 408 · 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 √441? =
2. 2.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
3. 3.What is 23²? =
4. 4.A square garden has an area of 81 square m. How long is each side (in m)?
5. 5.Which of these is a perfect square? (a) 336 (b) 324 (c) 345
6. 6.What is √7744? =
7. 7.What is 22²? =
8. 8.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
9. 9.What is √1936? =
10. 10.A square garden has an area of 324 square m. How long is each side (in m)?
11. 11.What is the smallest whole number by which 637 must be divided to get a perfect square?
12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 41²? =
15. 15.What is the smallest whole number by which 224 must be divided to get a perfect square?
16. 16.What is 77²? =
17. 17.What is 91²? =
18. 18.A square garden has an area of 676 square m. How long is each side (in m)?
19. 19.What is √8464? =
20. 20.How many whole numbers lie between 9² and 10²?
21. 21.What is 34²? =
22. 22.What is √729? =
23. 23.A square garden has an area of 1444 square m. How long is each side (in m)?
24. 24.What is √361? =
25. 25.How many whole numbers lie between 37² and 38²?
26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the smallest whole number by which 1215 must be divided to get a perfect square?
30. 30.What is √6889? =
31. 31.What is √8100? =
32. 32.Which of these is a perfect square? (a) 484 (b) 525 (c) 517
33. 33.A square garden has an area of 576 square m. How long is each side (in m)?
34. 34.Which of these is a perfect square? (a) 289 (b) 314 (c) 291
35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 2304 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 12 must be divided to get a perfect square?
38. 38.What is √1296? =
39. 39.What is √2209? =
40. 40.Which of these is a perfect square? (a) 127 (b) 142 (c) 121

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