Question

Which expression is equal to 2 sqrt 54 - 4 sqrt 24

Answer 1

Hello!

First, make it so the number under the root symbol is the same. You can do this with the product property of square roots. This property states that if you turn the number under a square root into a product of 2 numbers, you can extract them under different root symbols. For example,$\sqrt{10}=\sqrt{2*5}  =\sqrt{2} *\sqr5}$.

Now, we are looking so the numbers under the square root are the same. To do this, look for the smallest number where the other number split is a square number. This will allow us to square root that number.

$2\sqrt{54} -4\sqrt{24}$

$2\sqrt{9 * 6} -4\sqrt{4 * 6}$

$(2\sqrt{9} *\sqrt{6})  - (4\sqrt{4} *\sqrt{6} )$

Now, sqrt the square number, and simplify.

$(2\sqrt{9} *\sqrt{6})  - (4\sqrt{4} *\sqrt{6} )$

$(2*3 *\sqrt{6})  - (4*2 *\sqrt{6} )$

$(6\sqrt{6})  - (8\sqrt{6} )$

And finally, subtract.

$(6\sqrt{6})  - (8\sqrt{6} )$

$-2\sqrt{6}$

Therefore, your answer is the third choice.

Hope this helps!