Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 644 · 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.Which of these is a perfect square? (a) 314 (b) 289 (c) 308
2. 2.Which of these is a perfect square? (a) 116 (b) 100 (c) 117
3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √5929? =
5. 5.What is 31²? =
6. 6.What is √4356? =
7. 7.A square garden has an area of 1849 square m. How long is each side (in m)?
8. 8.Which of these is a perfect square? (a) 1637 (b) 1624 (c) 1600
9. 9.What is √8464? =
10. 10.A square garden has an area of 1156 square m. How long is each side (in m)?
11. 11.A square garden has an area of 1444 square m. How long is each side (in m)?
12. 12.What is √2304? =
13. 13.What is √4900? =
14. 14.What is 58²? =
15. 15.What is √121? =
16. 16.Which of these is a perfect square? (a) 944 (b) 900 (c) 936
17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 1407 (b) 1369 (c) 1391
21. 21.A square garden has an area of 729 square m. How long is each side (in m)?
22. 22.Which of these is a perfect square? (a) 221 (b) 196 (c) 209
23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the smallest whole number by which 32 must be divided to get a perfect square?
25. 25.What is 79²? =
26. 26.A square garden has an area of 676 square m. How long is each side (in m)?
27. 27.How many whole numbers lie between 46² and 47²?
28. 28.Which of these is a perfect square? (a) 1538 (b) 1559 (c) 1521
29. 29.What is 27²? =
30. 30.What is 91²? =
31. 31.How many whole numbers lie between 16² and 17²?
32. 32.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
33. 33.What is 80²? =
34. 34.What is 50²? =
35. 35.What is 41²? =
36. 36.What is the smallest whole number by which 567 must be divided to get a perfect square?
37. 37.Which of these is a perfect square? (a) 846 (b) 841 (c) 860
38. 38.A square garden has an area of 169 square m. How long is each side (in m)?
39. 39.What is √1024? =
40. 40.What is 76²? =

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