Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 397 · 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 22 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 50²? =
3. 3.What is 58²? =
4. 4.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
5. 5.What is √169? =
6. 6.Which of these is a perfect square? (a) 344 (b) 324 (c) 335
7. 7.How many whole numbers lie between 42² and 43²?
8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
9. 9.How many whole numbers lie between 7² and 8²?
10. 10.What is 40²? =
11. 11.A square garden has an area of 576 square m. How long is each side (in m)?
12. 12.How many whole numbers lie between 17² and 18²?
13. 13.What is 23²? =
14. 14.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
15. 15.How many whole numbers lie between 24² and 25²?
16. 16.What is 26²? =
17. 17.How many whole numbers lie between 10² and 11²?
18. 18.How many whole numbers lie between 9² and 10²?
19. 19.How many whole numbers lie between 22² and 23²?
20. 20.What is √2601? =
21. 21.What is 76²? =
22. 22.Which of these is a perfect square? (a) 529 (b) 560 (c) 540
23. 23.What is √676? =
24. 24.What is the smallest whole number by which 216 must be divided to get a perfect square?
25. 25.What is √144? =
26. 26.How many whole numbers lie between 16² and 17²?
27. 27.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
28. 28.What is 87²? =
29. 29.What is √361? =
30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 21²? =
32. 32.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
33. 33.Which of these is a perfect square? (a) 361 (b) 380 (c) 378
34. 34.A square garden has an area of 64 square m. How long is each side (in m)?
35. 35.What is √5929? =
36. 36.A square garden has an area of 676 square m. How long is each side (in m)?
37. 37.A square garden has an area of 2304 square m. How long is each side (in m)?
38. 38.What is 13²? =
39. 39.What is √4900? =
40. 40.What is √729? =

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