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 :)
