Answer:
Option C is Correct
Step-by-step explanation:
Given:
[tex]\sqrt{648}= \sqrt{2^a.3^b}[/tex]
We need to check the values of a and b such that the given equation remains true
1. a= 3 and b=2
[tex]\sqrt{648}= \sqrt{2^3.3^2}\\25.4 = \sqrt{72}\\25.4 \neq 8.4[/tex]
So, Option A is incorrect
2. a=2 and b= 3
[tex]\sqrt{648}= \sqrt{2^2.3^3}\\25.4 = \sqrt{108}\\25.4 \neq 10.3[/tex]
So, Option B is incorrect
3. a=3, b=4
[tex]\sqrt{648}= \sqrt{2^3.3^4}\\25.4 = \sqrt{648}\\25.4= 25.4[/tex]
So, Option C is correct.
4. a= 4, b=3
[tex]\sqrt{648}= \sqrt{2^4.3^3}\\25.4 = \sqrt{432}\\25.4 \neq 20.7[/tex]
So, Option D is incorrect.
