Hey there! :)
[tex] 6\sqrt{3} + 5 \sqrt{12} [/tex]
In order to add these together, we must simplify the square roots.
[tex]6 \sqrt{3} [/tex] is already in simplest terms, but [tex]5 \sqrt{12} [/tex] is not.
So, let's start simplifying it!
[tex] \sqrt{12} = ?[/tex]
We need to take out any squares within 12.
So, if we branch out 12, we know that 4 × 3 = 12
√4 = 2. So, we can take out 2 and be left with √3.
Since the original square is 5√12, we MUST multiply 5 by 2.
[tex]5*2 \sqrt{3} = 10 \sqrt{3} [/tex]
So, using the simplified number of 5 root 12, we now can add this to 6 root 3.
[tex]6 \sqrt{3} + 10 \sqrt{3} = 16 \sqrt{3} [/tex]
So, our final answer is : [tex]16 \sqrt{3} [/tex]
~Hope I helped!~
