Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 658 · 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 the smallest whole number by which 245 must be multiplied to get a perfect square?
2. 2.A square garden has an area of 625 square m. How long is each side (in m)?
3. 3.How many whole numbers lie between 19² and 20²?
4. 4.What is √3600? =
5. 5.What is √1764? =
6. 6.Which of these is a perfect square? (a) 784 (b) 788 (c) 816
7. 7.A square garden has an area of 1849 square m. How long is each side (in m)?
8. 8.What is 31²? =
9. 9.What is 75²? =
10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 685 (b) 681 (c) 676
12. 12.What is 89²? =
13. 13.What is 72²? =
14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √484? =
16. 16.A square garden has an area of 1936 square m. How long is each side (in m)?
17. 17.A square garden has an area of 3481 square m. How long is each side (in m)?
18. 18.How many whole numbers lie between 14² and 15²?
19. 19.What is √3844? =
20. 20.What is the smallest whole number by which 60 must be divided to get a perfect square?
21. 21.What is 41²? =
22. 22.How many whole numbers lie between 38² and 39²?
23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
24. 24.What is 62²? =
25. 25.What is the smallest whole number by which 294 must be divided to get a perfect square?
26. 26.Which of these is a perfect square? (a) 1254 (b) 1225 (c) 1258
27. 27.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
28. 28.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
29. 29.What is 14²? =
30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 46²? =
32. 32.A square garden has an area of 729 square m. How long is each side (in m)?
33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √7569? =
36. 36.How many whole numbers lie between 10² and 11²?
37. 37.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
38. 38.A square garden has an area of 841 square m. How long is each side (in m)?
39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
40. 40.What is √9025? =

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