# How do you evaluate 2\sqrt { 48} + \sqrt { 24} - 3\sqrt { 75} + \sqrt { 96}?

Jun 29, 2017

Simply input into a calculator - mind the brackets. Or simplify and input into calculator - disregard the brackets.

#### Explanation:

All you have to do is input these values into a calculator. Be sure to use brackets accordingly.

Or, you can simplify and do the same (input into calculator - no need for brackets).

To simplify, we have to add like terms. Like terms in a radical in an expression are variables with the same number under a radical.

First, let's "break up" the radicals into simpler terms. We do this by dividing the variable by perfect squares.

$2 \sqrt{48} + \sqrt{24} - 3 \sqrt{75} + \sqrt{96}$

$= 2 \sqrt{16} \sqrt{3} + \sqrt{4} \sqrt{6} - 3 \sqrt{25} \sqrt{3} + \sqrt{16} \sqrt{6}$

Now, with perfect squares under the radical, we can simplify it.

$= 2 \left(4\right) \sqrt{3} + \left(2\right) \sqrt{6} - 3 \left(5\right) \sqrt{3} + \left(4\right) \sqrt{6}$

Simplify it further (it's just the coefficient).

$= 8 \sqrt{3} + 2 \sqrt{6} - 15 \sqrt{3} + 4 \sqrt{6}$

Now we can add like terms. Remember, a number under a radical is considered as one term.

$= - 7 \sqrt{3} + 6 \sqrt{6}$

I'm going to rearrange this so the positive radical is first. It's just for better "communication".

$= 6 \sqrt{6} - 7 \sqrt{3}$

We can double check our work by comparing their values after evaluating them.

$2 \sqrt{48} + \sqrt{24} - 3 \sqrt{75} + \sqrt{96} = 6 \sqrt{6} - 7 \sqrt{3}$

$2.572582804 = 2.572582804$

They equal each other thus, not only was it simplified, we also evaluated it.

Hope this helps :)