Question

What values of a and b make the equation true? Screenshots attached, please help!

Answer 1

Option C is Correct

Explanation:

Given:

`√(648)= √(2^a.3^b)`

We need to check the values of a and b such that the given equation remains true

1. a= 3 and b=2

`√(648)= √(2^3.3^2)\\25.4 = √(72)\\25.4 \\eq 8.4`

So, Option A is incorrect

2. a=2 and b= 3

`√(648)= √(2^2.3^3)\\25.4 = √(108)\\25.4 \\eq 10.3`

So, Option B is incorrect

3. a=3, b=4

`√(648)= √(2^3.3^4)\\25.4 = √(648)\\25.4= 25.4`

So, Option C is correct.

4. a= 4, b=3

`√(648)= √(2^4.3^3)\\25.4 = √(432)\\25.4 \\eq 20.7`

So, Option D is incorrect.