Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 42 · 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 961 square m. How long is each side (in m)?
2. 2.What is the smallest whole number by which 24 must be divided to get a perfect square?
3. 3.A square garden has an area of 169 square m. How long is each side (in m)?
4. 4.What is 91²? =
5. 5.What is √1024? =
6. 6.What is 16²? =
7. 7.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
8. 8.Which of these is a perfect square? (a) 900 (b) 902 (c) 913
9. 9.What is 81²? =
10. 10.What is the smallest whole number by which 540 must be divided to get a perfect square?
11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 49²? =
13. 13.A square garden has an area of 225 square m. How long is each side (in m)?
14. 14.What is √841? =
15. 15.What is √676? =
16. 16.What is √625? =
17. 17.A square garden has an area of 1936 square m. How long is each side (in m)?
18. 18.What is 38²? =
19. 19.A square garden has an area of 2500 square m. How long is each side (in m)?
20. 20.What is 44²? =
21. 21.What is the smallest whole number by which 567 must be divided to get a perfect square?
22. 22.What is 97²? =
23. 23.What is 71²? =
24. 24.What is the smallest whole number by which 20 must be divided to get a perfect square?
25. 25.How many whole numbers lie between 47² and 48²?
26. 26.What is 29²? =
27. 27.What is √1156? =
28. 28.A square garden has an area of 121 square m. How long is each side (in m)?
29. 29.What is 12²? =
30. 30.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 33²? =
32. 32.A square garden has an area of 289 square m. How long is each side (in m)?
33. 33.What is √400? =
34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 37²? =
36. 36.What is √6561? =
37. 37.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
39. 39.How many whole numbers lie between 21² and 22²?
40. 40.What is 64²? =

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