Question

Which expression is equal to 2√54−4√24?

​ √6 ​

​−√6 ​

−2√6

−11√6

Answer 1

-2√6 , because 2√54 - 4√24= 2√9•6 - 4√4•6 = 6√6 - 8√6 = -2√6

Answer 2

C.
`-2√( 6)`

Explanation:

We have been given an expression. We are asked to simplify the given expression.

`2√(54)-4√(24)`

First of all, we will factor out perfect square under the radicals as shown below:

`2√(9\cdot 6)-4√(4\cdot 6)`

`2√(3^2\cdot 6)-4√(2^2\cdot 6)`

Factor out perfect square:

`2\cdot 3√(6)-4\cdot 2√( 6)`

`6√(6)-8√( 6)`

Combine like terms:

`-2√( 6)`

Therefore, option C is the correct choice.