Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 46 · 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 √625? =
2. 2.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 95²? =
4. 4.A square garden has an area of 1156 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 10² and 11²?
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √1156? =
8. 8.What is 25²? =
9. 9.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
10. 10.What is the smallest whole number by which 20 must be divided to get a perfect square?
11. 11.Which of these is a perfect square? (a) 238 (b) 229 (c) 225
12. 12.Which of these is a perfect square? (a) 784 (b) 797 (c) 788
13. 13.Which of these is a perfect square? (a) 295 (b) 291 (c) 289
14. 14.A square garden has an area of 1936 square m. How long is each side (in m)?
15. 15.What is 22²? =
16. 16.A square garden has an area of 484 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 18² and 19²?
18. 18.How many whole numbers lie between 38² and 39²?
19. 19.What is 73²? =
20. 20.A square garden has an area of 2704 square m. How long is each side (in m)?
21. 21.Which of these is a perfect square? (a) 394 (b) 386 (c) 361
22. 22.What is √3969? =
23. 23.What is √7921? =
24. 24.What is √6561? =
25. 25.What is 79²? =
26. 26.What is 34²? =
27. 27.Which of these is a perfect square? (a) 1024 (b) 1064 (c) 1058
28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 1475 (b) 1490 (c) 1444
30. 30.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
31. 31.What is the smallest whole number by which 96 must be divided to get a perfect square?
32. 32.What is √1296? =
33. 33.What is √361? =
34. 34.What is √121? =
35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
36. 36.How many whole numbers lie between 12² and 13²?
37. 37.A square garden has an area of 100 square m. How long is each side (in m)?
38. 38.Which of these is a perfect square? (a) 331 (b) 355 (c) 324
39. 39.What is 80²? =
40. 40.What is 28²? =

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