Question

Simplify radical 147/4

Answer 1

To simplify the expression \(\sqrt{\frac{147}{4}}\), we can break it down as follows:

1. Use the property of square roots that states \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\):

\[
\sqrt{\frac{147}{4}} = \frac{\sqrt{147}}{\sqrt{4}}
\]

2. Calculate \(\sqrt{4}\):

\[
\sqrt{4} = 2
\]

So, we have:

\[
\sqrt{\frac{147}{4}} = \frac{\sqrt{147}}{2}
\]

3. Next, simplify \(\sqrt{147}\). We can factor \(147\) to find any perfect squares:

\[
147 = 49 \times 3 = 7^2 \times 3
\]

Thus:

\[
\sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \times \sqrt{3} = 7\sqrt{3}
\]

4. Put this back into the expression:

\[
\sqrt{\frac{147}{4}} = \frac{7\sqrt{3}}{2}
\]

Therefore, the simplified form of \(\sqrt{\frac{147}{4}}\) is:

\[
\frac{7\sqrt{3}}{2}
\]