Question

\sqrt(27)-:2\sqrt(45)

divide

Answer 1

To simplify \(\frac{\sqrt{27}}{2\sqrt{45}}\), we can start by simplifying the square roots in the expression.

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

2. **Simplify \(\sqrt{45}\)**:
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
\]

3. **Now substitute back into the expression**:
\[
\frac{\sqrt{27}}{2\sqrt{45}} = \frac{3\sqrt{3}}{2 \times 3\sqrt{5}} = \frac{3\sqrt{3}}{6\sqrt{5}}
\]

4. **We can simplify further**:
\[
\frac{3\sqrt{3}}{6\sqrt{5}} = \frac{1}{2} \cdot \frac{\sqrt{3}}{\sqrt{5}} = \frac{\sqrt{3}}{2\sqrt{5}} = \frac{\sqrt{3}}{2\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{15}}{10}
\]

So, the final simplified form of \(\frac{\sqrt{27}}{2\sqrt{45}}\) is:
\[
\frac{\sqrt{15}}{10}
\]