Question

What is the simplified form of the following expression? 2√27+√12-3√3-2√12

Answer 1

For this case we must simplify the following expression:

`2 \sqrt {27} + \sqrt {12} -3 \sqrt {3} -2 \sqrt {12}`

We have to:

`27 = 3 ^ 3 = 3 * 3 ^ 2\\12 = 4 * 3 = 2 ^ 2 * 3`

Rewriting the expression we have:

`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}`

Answer:

`\sqrt {3}`