Question 5 complete expression adding the radicals radical 12 plus 2 radical 27

Answer 1

To simplify the expression \( \sqrt{12} + 2\sqrt{27} \), we start by simplifying each radical.

1. Simplifying \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

2. Simplifying \( \sqrt{27} \): \[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3} \] So, \( 2\sqrt{27} = 2 \times 3\sqrt{3} = 6\sqrt{3} \).

Now, substituting these simplifications back into the expression, we have: \[ \sqrt{12} + 2\sqrt{27} = 2\sqrt{3} + 6\sqrt{3} \]

3. Combining like terms: \[ 2\sqrt{3} + 6\sqrt{3} = (2 + 6)\sqrt{3} = 8\sqrt{3} \]

Thus, the complete expression simplifies to: \[ \sqrt{12} + 2\sqrt{27} = 8\sqrt{3} \]