Question

12 times radical 12 + 2 * radical 27

Answer 1

To simplify the expression \( 12 \sqrt{12} + 2 \sqrt{27} \), we will first break down the square roots.

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

2. **So, \( 12 \sqrt{12} \) becomes**:
\[
12 \sqrt{12} = 12(2\sqrt{3}) = 24\sqrt{3}
\]

3. **Simplifying \( \sqrt{27} \)**:
\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \sqrt{3} = 3\sqrt{3}
\]

4. **So, \( 2 \sqrt{27} \) becomes**:
\[
2 \sqrt{27} = 2(3\sqrt{3}) = 6\sqrt{3}
\]

5. **Now, we combine both simplified parts**:
\[
12 \sqrt{12} + 2 \sqrt{27} = 24\sqrt{3} + 6\sqrt{3} = (24 + 6)\sqrt{3} = 30\sqrt{3}
\]

Thus, the simplified expression is:
\[
\boxed{30\sqrt{3}}
\]