For this case we must simplify the following expression:
[tex]2 \sqrt {27} + \sqrt {12} -3 \sqrt {3} -2 \sqrt {12}[/tex]
We have to:
[tex]27 = 3 ^ 3 = 3 * 3 ^ 2\\12 = 4 * 3 = 2 ^ 2 * 3[/tex]
Rewriting the expression we have:
[tex]2 \sqrt {3 * 3 ^ 2} + \sqrt {2 ^ 2 * 3} -3 \sqrt {3} -2 \sqrt {2 ^ 2 * 3} =\\2 * 3 \sqrt {3} +2 \sqrt {3} -3 \sqrt {3} -2 * 2 \sqrt {3} =\\6 \sqrt {3} +2 \sqrt {3} -3 \sqrt {3} -4 \sqrt {3} =\\8 \sqrt {3} -3 \sqrt {3} -4 \sqrt {3} =\\5 \sqrt {3} -4 \sqrt {3} =\\\sqrt {3}[/tex]
Answer:
[tex]\sqrt {3}[/tex]
