Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 120 · 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 3364 square m. How long is each side (in m)?
2. 2.What is 89²? =
3. 3.Which of these is a perfect square? (a) 177 (b) 192 (c) 169
4. 4.What is 39²? =
5. 5.What is √9801? =
6. 6.What is 22²? =
7. 7.Which of these is a perfect square? (a) 1156 (b) 1171 (c) 1195
8. 8.What is 62²? =
9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
10. 10.What is √1600? =
11. 11.How many whole numbers lie between 11² and 12²?
12. 12.What is 54²? =
13. 13.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
16. 16.What is √5776? =
17. 17.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
18. 18.What is √3364? =
19. 19.How many whole numbers lie between 17² and 18²?
20. 20.What is 85²? =
21. 21.What is 48²? =
22. 22.What is 57²? =
23. 23.What is the smallest whole number by which 360 must be divided to get a perfect square?
24. 24.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
25. 25.Which of these is a perfect square? (a) 644 (b) 625 (c) 670
26. 26.What is √3969? =
27. 27.How many whole numbers lie between 26² and 27²?
28. 28.What is 47²? =
29. 29.What is 66²? =
30. 30.What is √625? =
31. 31.What is √5041? =
32. 32.What is 84²? =
33. 33.What is √2209? =
34. 34.What is 83²? =
35. 35.What is 87²? =
36. 36.Which of these is a perfect square? (a) 410 (b) 418 (c) 400
37. 37.What is the smallest whole number by which 150 must be divided to get a perfect square?
38. 38.What is 41²? =
39. 39.A square garden has an area of 2809 square m. How long is each side (in m)?
40. 40.What is 33²? =

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