Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 656 · 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 √4900? =
2. 2.Which of these is a perfect square? (a) 275 (b) 256 (c) 281
3. 3.Which of these is a perfect square? (a) 795 (b) 784 (c) 816
4. 4.How many whole numbers lie between 41² and 42²?
5. 5.What is √784? =
6. 6.What is 29²? =
7. 7.What is 50²? =
8. 8.What is 19²? =
9. 9.Which of these is a perfect square? (a) 138 (b) 121 (c) 141
10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 400 square m. How long is each side (in m)?
12. 12.Which of these is a perfect square? (a) 1444 (b) 1469 (c) 1450
13. 13.What is 25²? =
14. 14.What is √1521? =
15. 15.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
17. 17.A square garden has an area of 1764 square m. How long is each side (in m)?
18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 69²? =
20. 20.What is 23²? =
21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
22. 22.What is √361? =
23. 23.What is √6241? =
24. 24.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
25. 25.What is √196? =
26. 26.What is √4761? =
27. 27.What is √5625? =
28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 68²? =
30. 30.Which of these is a perfect square? (a) 406 (b) 429 (c) 400
31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 1232 (b) 1225 (c) 1244
33. 33.A square garden has an area of 25 square m. How long is each side (in m)?
34. 34.What is √1024? =
35. 35.What is the smallest whole number by which 24 must be divided to get a perfect square?
36. 36.A square garden has an area of 169 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 252 must be divided to get a perfect square?
38. 38.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
39. 39.A square garden has an area of 961 square m. How long is each side (in m)?
40. 40.How many whole numbers lie between 46² and 47²?

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