Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 579 · 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 729 square m. How long is each side (in m)?
2. 2.What is √576? =
3. 3.What is √169? =
4. 4.A square garden has an area of 1369 square m. How long is each side (in m)?
5. 5.What is 16²? =
6. 6.Which of these is a perfect square? (a) 1239 (b) 1225 (c) 1254
7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
9. 9.A square garden has an area of 100 square m. How long is each side (in m)?
10. 10.A square garden has an area of 3481 square m. How long is each side (in m)?
11. 11.A square garden has an area of 1089 square m. How long is each side (in m)?
12. 12.Which of these is a perfect square? (a) 266 (b) 260 (c) 256
13. 13.Which of these is a perfect square? (a) 729 (b) 750 (c) 730
14. 14.Which of these is a perfect square? (a) 157 (b) 144 (c) 145
15. 15.What is √324? =
16. 16.Which of these is a perfect square? (a) 1202 (b) 1200 (c) 1156
17. 17.Which of these is a perfect square? (a) 243 (b) 225 (c) 238
18. 18.What is √4225? =
19. 19.What is 28²? =
20. 20.A square garden has an area of 144 square m. How long is each side (in m)?
21. 21.Which of these is a perfect square? (a) 350 (b) 335 (c) 324
22. 22.A square garden has an area of 81 square m. How long is each side (in m)?
23. 23.What is √2500? =
24. 24.What is 26²? =
25. 25.What is √5476? =
26. 26.What is the smallest whole number by which 208 must be divided to get a perfect square?
27. 27.What is 55²? =
28. 28.What is 68²? =
29. 29.What is √529? =
30. 30.What is 41²? =
31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
32. 32.A square garden has an area of 1296 square m. How long is each side (in m)?
33. 33.A square garden has an area of 1521 square m. How long is each side (in m)?
34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
35. 35.A square garden has an area of 225 square m. How long is each side (in m)?
36. 36.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 13²? =
38. 38.What is 66²? =
39. 39.What is 57²? =
40. 40.How many whole numbers lie between 7² and 8²?

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