Answer:
Option (c) is correct.
a = 3 and b = 4
Step-by-step explanation:
Given : [tex]\sqrt{648}=\sqrt{2^a\cdot3^b}[/tex]
We have to find the values of a and b and choose the correct options from the given options.
Consider [tex]\sqrt{648}[/tex]
We first factorize 648 that is writing 648 as products of its prime factors.
648 can be written as 8 × 81
breaking 8 as product of 2 and 81 as product of 3.
We get,
[tex]684=2^3\times 3^4[/tex]
Also,
[tex]\sqrt{648}=\sqrt{2^3\cdot3^4}[/tex]
Thus, a = 3 and b = 4
Option (c) is correct.
