Question

What values of a and b make the equation true? sqrt(648)=sqrt(2^a•3^b)

Answer 1

ANSWER

The value of a and b are:

$a=3,b=4$

EXPLANATION

The expression given to us is

$\sqrt{648} = \sqrt{ {2}^{a} \times {3}^{b} }$

We square both sides of the equation to obtain

$648= {2}^{a} \times {3}^{b}$

We now find the prime factorization of 648 to obtain,

${2}^{3} \times {3}^{4} = {2}^{a} \times {3}^{b}$

We now compare the exponents on both sides of the equation to obtain,

$a=3,b=4$

Therefore the correct option is C