Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 381 · 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 sum of the first 27 odd numbers (1 + 3 + 5 + …)?
2. 2.What is √400? =
3. 3.What is √2500? =
4. 4.What is √6889? =
5. 5.Which of these is a perfect square? (a) 1374 (b) 1369 (c) 1431
6. 6.What is √9025? =
7. 7.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
8. 8.Which of these is a perfect square? (a) 387 (b) 374 (c) 361
9. 9.A square garden has an area of 2809 square m. How long is each side (in m)?
10. 10.What is √3721? =
11. 11.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
12. 12.What is √5184? =
13. 13.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 22²? =
15. 15.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
16. 16.What is √4900? =
17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
18. 18.A square garden has an area of 900 square m. How long is each side (in m)?
19. 19.What is √3481? =
20. 20.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 873 (b) 881 (c) 841
22. 22.A square garden has an area of 1444 square m. How long is each side (in m)?
23. 23.A square garden has an area of 1369 square m. How long is each side (in m)?
24. 24.What is 69²? =
25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
26. 26.What is √6400? =
27. 27.Which of these is a perfect square? (a) 226 (b) 238 (c) 225
28. 28.What is the smallest whole number by which 490 must be divided to get a perfect square?
29. 29.A square garden has an area of 2116 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 25² and 26²?
31. 31.What is √1600? =
32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
33. 33.What is 63²? =
34. 34.What is √9409? =
35. 35.How many whole numbers lie between 15² and 16²?
36. 36.What is √784? =
37. 37.What is 53²? =
38. 38.How many whole numbers lie between 35² and 36²?
39. 39.What is the smallest whole number by which 27 must be divided to get a perfect square?
40. 40.A square garden has an area of 676 square m. How long is each side (in m)?

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