Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 251 · 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 89²? =
2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √900? =
4. 4.A square garden has an area of 2304 square m. How long is each side (in m)?
5. 5.Which of these is a perfect square? (a) 450 (b) 445 (c) 441
6. 6.What is √5184? =
7. 7.What is 54²? =
8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 80²? =
10. 10.Which of these is a perfect square? (a) 625 (b) 649 (c) 672
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 1444 (b) 1491 (c) 1519
13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 34²? =
15. 15.A square garden has an area of 2704 square m. How long is each side (in m)?
16. 16.How many whole numbers lie between 47² and 48²?
17. 17.What is √1296? =
18. 18.Which of these is a perfect square? (a) 353 (b) 349 (c) 324
19. 19.What is the smallest whole number by which 24 must be divided to get a perfect square?
20. 20.Which of these is a perfect square? (a) 150 (b) 147 (c) 144
21. 21.Which of these is a perfect square? (a) 407 (b) 400 (c) 437
22. 22.What is 78²? =
23. 23.What is √6400? =
24. 24.A square garden has an area of 361 square m. How long is each side (in m)?
25. 25.A square garden has an area of 529 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 637 must be divided to get a perfect square?
27. 27.What is 39²? =
28. 28.What is 79²? =
29. 29.How many whole numbers lie between 41² and 42²?
30. 30.How many whole numbers lie between 12² and 13²?
31. 31.A square garden has an area of 1849 square m. How long is each side (in m)?
32. 32.What is √841? =
33. 33.A square garden has an area of 625 square m. How long is each side (in m)?
34. 34.How many whole numbers lie between 32² and 33²?
35. 35.A square garden has an area of 1521 square m. How long is each side (in m)?
36. 36.A square garden has an area of 25 square m. How long is each side (in m)?
37. 37.What is √2116? =
38. 38.A square garden has an area of 289 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 1125 (b) 1123 (c) 1089
40. 40.What is √169? =

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