Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 248 · 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.How many whole numbers lie between 10² and 11²?
2. 2.What is √1024? =
3. 3.What is 64²? =
4. 4.How many whole numbers lie between 33² and 34²?
5. 5.How many whole numbers lie between 32² and 33²?
6. 6.Which of these is a perfect square? (a) 169 (b) 172 (c) 177
7. 7.Which of these is a perfect square? (a) 244 (b) 225 (c) 249
8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 44²? =
10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 91²? =
12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √2116? =
14. 14.What is 85²? =
15. 15.What is 18²? =
16. 16.How many whole numbers lie between 11² and 12²?
17. 17.How many whole numbers lie between 41² and 42²?
18. 18.What is 62²? =
19. 19.What is the smallest whole number by which 40 must be divided to get a perfect square?
20. 20.What is 75²? =
21. 21.What is 22²? =
22. 22.A square garden has an area of 1936 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 400 (b) 404 (c) 409
24. 24.Which of these is a perfect square? (a) 308 (b) 307 (c) 289
25. 25.What is 30²? =
26. 26.Which of these is a perfect square? (a) 1220 (b) 1156 (c) 1214
27. 27.What is 13²? =
28. 28.What is 61²? =
29. 29.A square garden has an area of 2025 square m. How long is each side (in m)?
30. 30.What is 45²? =
31. 31.Which of these is a perfect square? (a) 841 (b) 861 (c) 859
32. 32.What is the smallest whole number by which 640 must be divided to get a perfect square?
33. 33.What is 33²? =
34. 34.Which of these is a perfect square? (a) 361 (b) 394 (c) 384
35. 35.A square garden has an area of 400 square m. How long is each side (in m)?
36. 36.A square garden has an area of 144 square m. How long is each side (in m)?
37. 37.What is √361? =
38. 38.Which of these is a perfect square? (a) 532 (b) 573 (c) 529
39. 39.How many whole numbers lie between 17² and 18²?
40. 40.How many whole numbers lie between 35² and 36²?

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