Question

Express in simplest radical form.
9, square root of, 72, end square root, plus, 3, square root of, 2, end square root
9
72
​
+3
2
​

Answer 1

To simplify the expression \( 9\sqrt{72} + 3\sqrt{2} \), we start by simplifying \( \sqrt{72} \).

1. **Simplify \(\sqrt{72}\)**:

\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}
\]

2. **Substitute back into the expression**:

Now we substitute \( \sqrt{72} \) back into the expression:

\[
9\sqrt{72} = 9 \cdot 6\sqrt{2} = 54\sqrt{2}
\]

3. **Combine the terms**:

Now we can rewrite the full expression:

\[
9\sqrt{72} + 3\sqrt{2} = 54\sqrt{2} + 3\sqrt{2}
\]

Now we can combine like terms:

\[
54\sqrt{2} + 3\sqrt{2} = (54 + 3)\sqrt{2} = 57\sqrt{2}
\]

Thus, the simplified expression is

\[
\boxed{57\sqrt{2}}
\]