Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 173 · 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 √144? =
2. 2.What is the smallest whole number by which 320 must be divided to get a perfect square?
3. 3.A square garden has an area of 900 square m. How long is each side (in m)?
4. 4.Which of these is a perfect square? (a) 1444 (b) 1482 (c) 1488
5. 5.What is 99²? =
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 25 square m. How long is each side (in m)?
8. 8.What is √1369? =
9. 9.Which of these is a perfect square? (a) 1039 (b) 1024 (c) 1085
10. 10.What is 21²? =
11. 11.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
12. 12.How many whole numbers lie between 19² and 20²?
13. 13.How many whole numbers lie between 21² and 22²?
14. 14.What is 14²? =
15. 15.What is √729? =
16. 16.How many whole numbers lie between 11² and 12²?
17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
18. 18.A square garden has an area of 324 square m. How long is each side (in m)?
19. 19.What is 33²? =
20. 20.What is √7225? =
21. 21.What is 72²? =
22. 22.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √1681? =
24. 24.What is √6400? =
25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
27. 27.A square garden has an area of 2209 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 50² and 51²?
29. 29.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 515 (b) 492 (c) 484
31. 31.Which of these is a perfect square? (a) 193 (b) 169 (c) 183
32. 32.Which of these is a perfect square? (a) 841 (b) 869 (c) 885
33. 33.A square garden has an area of 1936 square m. How long is each side (in m)?
34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √2704? =
38. 38.Which of these is a perfect square? (a) 256 (b) 279 (c) 278
39. 39.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
40. 40.What is 82²? =

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