Question

What values of a and b make the equation true? the square root of 648 = square root of 2^a * 3^b

Answer 1

Answer: OPTION C

Step-by-step explanation:

To solve the exercise you must descompose the number 648 into its prime factors, as you can see below:

$648=2*2*2*3*3*3*3$

You can rewrite the above as following:

$648=2^3*3^4$

Then:

$\sqrt{648}=\sqrt{2^3*3^4}$

Therefore, as you can see, the value of  a and b are the following:

$a=3,b=4$

Answer 2

Answer:

The correct answer option is C. a=3, b=4.

Step-by-step explanation:

We are given the following expression and we need to determine whether which of the values of $a$ and $b$ should be used to make the equation true:

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

A. a=3, b=2:

$\sqrt { 2 ^ 3 \times 3 ^ 2 } = \sqrt { 72 }$

B.  a=2, b=3:

$\sqrt { 2 ^ 2 \times 3 ^ 3 } = \sqrt { 108 }$

C. a=3, b=4 :

$\sqrt { 2 ^ 3 \times 3 ^ 4 } = \sqrt { 648 }$

D. a=4, b=3:

$\sqrt { 2 ^ 4 \times 3 ^ 3 } = \sqrt { 432 }$

Therefore, the correct answer option is C. a=3, b=4.