Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 24 · 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 √256? =
2. 2.A square garden has an area of 784 square m. How long is each side (in m)?
3. 3.What is 89²? =
4. 4.What is the smallest whole number by which 162 must be divided to get a perfect square?
5. 5.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
6. 6.Which of these is a perfect square? (a) 704 (b) 676 (c) 715
7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
8. 8.A square garden has an area of 196 square m. How long is each side (in m)?
9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 1089 square m. How long is each side (in m)?
11. 11.Which of these is a perfect square? (a) 624 (b) 594 (c) 576
12. 12.What is √361? =
13. 13.Which of these is a perfect square? (a) 362 (b) 381 (c) 361
14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √1156? =
16. 16.What is √2116? =
17. 17.What is √3025? =
18. 18.How many whole numbers lie between 47² and 48²?
19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
20. 20.What is 15²? =
21. 21.Which of these is a perfect square? (a) 1521 (b) 1548 (c) 1526
22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 33²? =
24. 24.A square garden has an area of 225 square m. How long is each side (in m)?
25. 25.Which of these is a perfect square? (a) 349 (b) 337 (c) 324
26. 26.What is 52²? =
27. 27.What is the smallest whole number by which 539 must be divided to get a perfect square?
28. 28.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
30. 30.What is 46²? =
31. 31.How many whole numbers lie between 10² and 11²?
32. 32.How many whole numbers lie between 21² and 22²?
33. 33.What is 35²? =
34. 34.Which of these is a perfect square? (a) 1240 (b) 1287 (c) 1225
35. 35.How many whole numbers lie between 49² and 50²?
36. 36.A square garden has an area of 1764 square m. How long is each side (in m)?
37. 37.Which of these is a perfect square? (a) 256 (b) 282 (c) 281
38. 38.Which of these is a perfect square? (a) 841 (b) 890 (c) 876
39. 39.What is √1681? =
40. 40.What is the smallest whole number by which 28 must be divided to get a perfect square?

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