Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 669 · 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 √2916? =
2. 2.Which of these is a perfect square? (a) 225 (b) 231 (c) 234
3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 372 (b) 361 (c) 394
5. 5.What is the smallest whole number by which 325 must be divided to get a perfect square?
6. 6.Which of these is a perfect square? (a) 725 (b) 721 (c) 676
7. 7.What is √9025? =
8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 38²? =
10. 10.Which of these is a perfect square? (a) 1675 (b) 1612 (c) 1600
11. 11.What is √1600? =
12. 12.A square garden has an area of 2809 square m. How long is each side (in m)?
13. 13.A square garden has an area of 2304 square m. How long is each side (in m)?
14. 14.A square garden has an area of 2601 square m. How long is each side (in m)?
15. 15.What is 13²? =
16. 16.Which of these is a perfect square? (a) 305 (b) 298 (c) 289
17. 17.A square garden has an area of 3481 square m. How long is each side (in m)?
18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
19. 19.How many whole numbers lie between 50² and 51²?
20. 20.A square garden has an area of 529 square m. How long is each side (in m)?
21. 21.A square garden has an area of 900 square m. How long is each side (in m)?
22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √1024? =
24. 24.What is 78²? =
25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 23²? =
27. 27.What is 48²? =
28. 28.What is 24²? =
29. 29.How many whole numbers lie between 16² and 17²?
30. 30.What is 17²? =
31. 31.What is the smallest whole number by which 250 must be divided to get a perfect square?
32. 32.How many whole numbers lie between 8² and 9²?
33. 33.What is √4225? =
34. 34.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
35. 35.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
36. 36.What is √2401? =
37. 37.How many whole numbers lie between 5² and 6²?
38. 38.Which of these is a perfect square? (a) 1304 (b) 1325 (c) 1296
39. 39.What is 59²? =
40. 40.What is 20²? =

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