Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 367 · 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.A square garden has an area of 1444 square m. How long is each side (in m)?
2. 2.A square garden has an area of 49 square m. How long is each side (in m)?
3. 3.What is the smallest whole number by which 80 must be divided to get a perfect square?
4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 49²? =
6. 6.What is 43²? =
7. 7.What is 81²? =
8. 8.What is 53²? =
9. 9.A square garden has an area of 324 square m. How long is each side (in m)?
10. 10.Which of these is a perfect square? (a) 430 (b) 400 (c) 415
11. 11.Which of these is a perfect square? (a) 318 (b) 317 (c) 289
12. 12.A square garden has an area of 1849 square m. How long is each side (in m)?
13. 13.What is 63²? =
14. 14.What is the smallest whole number by which 98 must be divided to get a perfect square?
15. 15.Which of these is a perfect square? (a) 168 (b) 160 (c) 144
16. 16.What is 20²? =
17. 17.A square garden has an area of 289 square m. How long is each side (in m)?
18. 18.How many whole numbers lie between 49² and 50²?
19. 19.Which of these is a perfect square? (a) 866 (b) 869 (c) 841
20. 20.What is √6241? =
21. 21.A square garden has an area of 1024 square m. How long is each side (in m)?
22. 22.What is 58²? =
23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
24. 24.How many whole numbers lie between 46² and 47²?
25. 25.A square garden has an area of 2209 square m. How long is each side (in m)?
26. 26.What is √4900? =
27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √2209? =
29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
30. 30.How many whole numbers lie between 38² and 39²?
31. 31.What is 18²? =
32. 32.What is √400? =
33. 33.Which of these is a perfect square? (a) 1472 (b) 1484 (c) 1444
34. 34.What is 35²? =
35. 35.A square garden has an area of 3600 square m. How long is each side (in m)?
36. 36.What is 96²? =
37. 37.A square garden has an area of 400 square m. How long is each side (in m)?
38. 38.What is 23²? =
39. 39.A square garden has an area of 100 square m. How long is each side (in m)?
40. 40.Which of these is a perfect square? (a) 716 (b) 676 (c) 713

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