Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 489 · 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 the smallest whole number by which 18 must be multiplied to get a perfect square?
2. 2.Which of these is a perfect square? (a) 361 (b) 371 (c) 380
3. 3.A square garden has an area of 196 square m. How long is each side (in m)?
4. 4.How many whole numbers lie between 17² and 18²?
5. 5.What is 85²? =
6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √6889? =
8. 8.What is √484? =
9. 9.A square garden has an area of 361 square m. How long is each side (in m)?
10. 10.What is 45²? =
11. 11.Which of these is a perfect square? (a) 198 (b) 196 (c) 212
12. 12.How many whole numbers lie between 9² and 10²?
13. 13.What is √8649? =
14. 14.What is 89²? =
15. 15.What is 31²? =
16. 16.What is the smallest whole number by which 75 must be divided to get a perfect square?
17. 17.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
18. 18.What is 70²? =
19. 19.What is 82²? =
20. 20.What is √625? =
21. 21.Which of these is a perfect square? (a) 792 (b) 784 (c) 795
22. 22.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √784? =
24. 24.Which of these is a perfect square? (a) 676 (b) 684 (c) 690
25. 25.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
26. 26.What is the smallest whole number by which 18 must be divided to get a perfect square?
27. 27.A square garden has an area of 1444 square m. How long is each side (in m)?
28. 28.What is 33²? =
29. 29.Which of these is a perfect square? (a) 266 (b) 261 (c) 256
30. 30.How many whole numbers lie between 19² and 20²?
31. 31.A square garden has an area of 1849 square m. How long is each side (in m)?
32. 32.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
33. 33.What is √144? =
34. 34.What is the smallest whole number by which 180 must be divided to get a perfect square?
35. 35.What is √3844? =
36. 36.How many whole numbers lie between 34² and 35²?
37. 37.How many whole numbers lie between 16² and 17²?
38. 38.How many whole numbers lie between 11² and 12²?
39. 39.What is √8100? =
40. 40.Which of these is a perfect square? (a) 1089 (b) 1106 (c) 1121

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