Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 58 · 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 1296 square m. How long is each side (in m)?
2. 2.What is the smallest whole number by which 208 must be divided to get a perfect square?
3. 3.A square garden has an area of 36 square m. How long is each side (in m)?
4. 4.What is √9409? =
5. 5.Which of these is a perfect square? (a) 468 (b) 453 (c) 441
6. 6.How many whole numbers lie between 36² and 37²?
7. 7.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
8. 8.What is √3721? =
9. 9.What is 90²? =
10. 10.What is √4225? =
11. 11.What is 50²? =
12. 12.What is 31²? =
13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 65²? =
15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
16. 16.What is 60²? =
17. 17.What is √8649? =
18. 18.What is √2916? =
19. 19.A square garden has an area of 441 square m. How long is each side (in m)?
20. 20.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
21. 21.A square garden has an area of 64 square m. How long is each side (in m)?
22. 22.Which of these is a perfect square? (a) 112 (b) 100 (c) 102
23. 23.How many whole numbers lie between 37² and 38²?
24. 24.What is 78²? =
25. 25.Which of these is a perfect square? (a) 181 (b) 179 (c) 169
26. 26.What is 93²? =
27. 27.Which of these is a perfect square? (a) 422 (b) 401 (c) 400
28. 28.What is 29²? =
29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 1558 (b) 1595 (c) 1521
31. 31.What is √4624? =
32. 32.What is 92²? =
33. 33.What is 66²? =
34. 34.What is 21²? =
35. 35.What is 12²? =
36. 36.Which of these is a perfect square? (a) 334 (b) 324 (c) 325
37. 37.A square garden has an area of 400 square m. How long is each side (in m)?
38. 38.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
39. 39.What is the smallest whole number by which 135 must be divided to get a perfect square?
40. 40.What is √5329? =

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