Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 169 · 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 8 must be multiplied to get a perfect square?
2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
3. 3.Which of these is a perfect square? (a) 484 (b) 485 (c) 525
4. 4.What is the smallest whole number by which 243 must be divided to get a perfect square?
5. 5.Which of these is a perfect square? (a) 357 (b) 350 (c) 324
6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
7. 7.What is 38²? =
8. 8.A square garden has an area of 3600 square m. How long is each side (in m)?
9. 9.What is √169? =
10. 10.What is 29²? =
11. 11.Which of these is a perfect square? (a) 575 (b) 562 (c) 529
12. 12.A square garden has an area of 144 square m. How long is each side (in m)?
13. 13.Which of these is a perfect square? (a) 185 (b) 169 (c) 175
14. 14.What is √6561? =
15. 15.What is 79²? =
16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
17. 17.What is √3844? =
18. 18.What is 39²? =
19. 19.What is 11²? =
20. 20.How many whole numbers lie between 17² and 18²?
21. 21.How many whole numbers lie between 15² and 16²?
22. 22.What is 66²? =
23. 23.How many whole numbers lie between 27² and 28²?
24. 24.A square garden has an area of 1849 square m. How long is each side (in m)?
25. 25.What is 40²? =
26. 26.What is 42²? =
27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
28. 28.A square garden has an area of 361 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 100 (b) 106 (c) 101
30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 78²? =
32. 32.What is √784? =
33. 33.What is √7569? =
34. 34.How many whole numbers lie between 50² and 51²?
35. 35.A square garden has an area of 841 square m. How long is each side (in m)?
36. 36.What is 56²? =
37. 37.What is the smallest whole number by which 8 must be divided to get a perfect square?
38. 38.What is √4900? =
39. 39.What is √4356? =
40. 40.What is √961? =

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