Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 361 · 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 √9025? =
2. 2.What is the smallest whole number by which 48 must be divided to get a perfect square?
3. 3.What is √3136? =
4. 4.A square garden has an area of 3481 square m. How long is each side (in m)?
5. 5.What is 79²? =
6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 1681 square m. How long is each side (in m)?
8. 8.What is √3025? =
9. 9.What is 61²? =
10. 10.Which of these is a perfect square? (a) 230 (b) 225 (c) 235
11. 11.What is 88²? =
12. 12.Which of these is a perfect square? (a) 484 (b) 485 (c) 488
13. 13.What is 70²? =
14. 14.Which of these is a perfect square? (a) 689 (b) 676 (c) 679
15. 15.What is 38²? =
16. 16.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
17. 17.Which of these is a perfect square? (a) 400 (b) 410 (c) 405
18. 18.What is √324? =
19. 19.What is √1156? =
20. 20.What is √625? =
21. 21.What is √3249? =
22. 22.Which of these is a perfect square? (a) 576 (b) 605 (c) 584
23. 23.What is the smallest whole number by which 245 must be divided to get a perfect square?
24. 24.What is 14²? =
25. 25.Which of these is a perfect square? (a) 144 (b) 167 (c) 153
26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
27. 27.Which of these is a perfect square? (a) 1146 (b) 1119 (c) 1089
28. 28.What is √121? =
29. 29.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
30. 30.What is the smallest whole number by which 1134 must be divided to get a perfect square?
31. 31.Which of these is a perfect square? (a) 1546 (b) 1592 (c) 1521
32. 32.What is √784? =
33. 33.How many whole numbers lie between 18² and 19²?
34. 34.What is the smallest whole number by which 8 must be divided to get a perfect square?
35. 35.What is the smallest whole number by which 60 must be divided to get a perfect square?
36. 36.What is 37²? =
37. 37.What is 21²? =
38. 38.What is √4624? =
39. 39.How many whole numbers lie between 12² and 13²?
40. 40.What is the smallest whole number by which 160 must be multiplied to get a perfect square?

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets