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

##### 1 Answer

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.

#2sqrt48 + sqrt24 - 3sqrt75 + sqrt96#

#=2sqrt16sqrt3 + sqrt4sqrt6 - 3sqrt25sqrt3 + sqrt16sqrt6#

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

#=2(4)sqrt3 + (2)sqrt6 - 3(5)sqrt3 + (4)sqrt6#

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

#=8sqrt3 + 2sqrt6 - 15sqrt3 + 4sqrt6#

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

#=-7sqrt3 + 6sqrt6#

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

#= 6sqrt6 -7sqrt3#

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

#2sqrt48 + sqrt24 - 3sqrt75 + sqrt96 = 6sqrt6 -7sqrt3#

#2.572582804 = 2.572582804#

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

Hope this helps :)