Question

Which of the following is equivalent to the expression below? √96 - √54+ √24

Answer 1

Explanation:

The expression that we have is:

`√(96)-√(54)+√(24)`

And we need to find the equivalent expression.

Step 1. The first step is to simplify the square roots by looking for multiplications that result in the number inside that square root, and that one of those numbers has an exact square root.

Let's start with the square root of 96, we can write 16x6 instead of 96:

And then, since 16 has an exact square root (which is 4) we further simplify the expression to:

`√(96)=4√(6)`

Step 2. We do the same for the other two square roots:

Step 3. Using these results, our expression now is:

`\sqrt[]{96}-√(54)+√(24)=4√(6)-3√(6)+2√(6)`

To find the equivalent expression, since now we have that all of the square roots have the same number inside (6) we can just make the operations with the numbers 4, -3, and 2, and the result is:

`4√(6)-3√(6)+2√(6)=\boxed{3√(6)}`

which is option D.

Answer:

D

`3√(6)`