Question

How do you solve this and what is the answer?

Answer 1

We want to get rid of the square root sign somehow, so let's isolate that term.

$2\sqrt{\frac{3x}{5}} + 3 = 11$
$2\sqrt{\frac{3x}{5}} = 11 - 3 = 8$
$\sqrt{\frac{3x}{5}} = 4$

Now, in order to 'undo' a root sign, we need to do the opposite to it, by squaring the term, but in order for it to remain the same, we need to square 4 as well.

$\frac{3x}{5} = 16$

Now, we can isolate the variable:
$3x = 5 \cdot 16 = 80$
$x = \frac{80}{3}$, and since we can't simplify this further, our final answer becomes:

$x = \frac{80}{3}$ or $x = 26\frac{2}{3}$