Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 611 · 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 1681 square m. How long is each side (in m)?
2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 46²? =
4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 2401 square m. How long is each side (in m)?
6. 6.A square garden has an area of 676 square m. How long is each side (in m)?
7. 7.What is √1024? =
8. 8.Which of these is a perfect square? (a) 582 (b) 576 (c) 601
9. 9.What is the smallest whole number by which 686 must be divided to get a perfect square?
10. 10.A square garden has an area of 1600 square m. How long is each side (in m)?
11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 324 (b) 349 (c) 337
13. 13.What is 83²? =
14. 14.A square garden has an area of 324 square m. How long is each side (in m)?
15. 15.A square garden has an area of 3364 square m. How long is each side (in m)?
16. 16.What is 11²? =
17. 17.What is 91²? =
18. 18.How many whole numbers lie between 34² and 35²?
19. 19.A square garden has an area of 64 square m. How long is each side (in m)?
20. 20.What is √9216? =
21. 21.How many whole numbers lie between 18² and 19²?
22. 22.How many whole numbers lie between 23² and 24²?
23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √441? =
25. 25.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
26. 26.Which of these is a perfect square? (a) 169 (b) 187 (c) 171
27. 27.What is 27²? =
28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 67²? =
30. 30.How many whole numbers lie between 5² and 6²?
31. 31.What is 35²? =
32. 32.Which of these is a perfect square? (a) 256 (b) 269 (c) 258
33. 33.What is 80²? =
34. 34.What is the smallest whole number by which 75 must be divided to get a perfect square?
35. 35.What is √121? =
36. 36.A square garden has an area of 1296 square m. How long is each side (in m)?
37. 37.What is 63²? =
38. 38.How many whole numbers lie between 35² and 36²?
39. 39.What is the smallest whole number by which 48 must be divided to get a perfect square?
40. 40.Which of these is a perfect square? (a) 1586 (b) 1521 (c) 1557

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