Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 676 · 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 √6724? =
2. 2.A square garden has an area of 2209 square m. How long is each side (in m)?
3. 3.Which of these is a perfect square? (a) 1623 (b) 1625 (c) 1600
4. 4.Which of these is a perfect square? (a) 389 (b) 366 (c) 361
5. 5.What is √2704? =
6. 6.How many whole numbers lie between 40² and 41²?
7. 7.What is √9409? =
8. 8.What is √4624? =
9. 9.What is √7569? =
10. 10.What is √3136? =
11. 11.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 37²? =
13. 13.What is 31²? =
14. 14.How many whole numbers lie between 49² and 50²?
15. 15.What is 50²? =
16. 16.What is 51²? =
17. 17.Which of these is a perfect square? (a) 213 (b) 196 (c) 223
18. 18.What is √900? =
19. 19.What is √2500? =
20. 20.What is 74²? =
21. 21.Which of these is a perfect square? (a) 430 (b) 404 (c) 400
22. 22.What is 49²? =
23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √8836? =
25. 25.What is 43²? =
26. 26.What is the smallest whole number by which 1215 must be divided to get a perfect square?
27. 27.A square garden has an area of 64 square m. How long is each side (in m)?
28. 28.What is 42²? =
29. 29.A square garden has an area of 784 square m. How long is each side (in m)?
30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
32. 32.What is 63²? =
33. 33.A square garden has an area of 121 square m. How long is each side (in m)?
34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √9216? =
36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
37. 37.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
40. 40.What is 40²? =

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