Question

Express in simplest radical form.
6, square root of, 8, end square root, plus, 5, square root of, 50, end square root
6
8
​
+5
50
​

Answer
Attempt 1 out of 5

Submit Answer
square root of, end square root
x
​

Answer 1

To simplify the expression \( 6\sqrt{8} + 5\sqrt{50} \), let's simplify each term separately.

1. **Simplifying \( \sqrt{8} \):**
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]
So,
\[
6\sqrt{8} = 6 \cdot 2\sqrt{2} = 12\sqrt{2}
\]

2. **Simplifying \( \sqrt{50} \):**
\[
\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]
Thus,
\[
5\sqrt{50} = 5 \cdot 5\sqrt{2} = 25\sqrt{2}
\]

Now, we can combine the simplified terms:
\[
12\sqrt{2} + 25\sqrt{2} = (12 + 25)\sqrt{2} = 37\sqrt{2}
\]

Therefore, the simplified expression is:
\[
\boxed{37\sqrt{2}}
\]