Question

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

A. a=3, b=2
B. a=2, b=3
C. a=3, b=4
D. a=4, b=3

Answer 1

Answer: OPTION C

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:

`√(648)=√(2^3*3^4)`

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

`a=3,b=4`

Answer 2

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

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 * 3 ^ b }`

A. a=3, b=2:

`\sqrt { 2 ^ 3 * 3 ^ 2 } = \sqrt { 72 }`

B. a=2, b=3:

`\sqrt { 2 ^ 2 * 3 ^ 3 } = \sqrt { 108 }`

C. a=3, b=4 :

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

D. a=4, b=3:

`\sqrt { 2 ^ 4 * 3 ^ 3 } = \sqrt { 432 }`

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