Question

Express in simplest radical form.
2, square root of, 150, end square root, plus, 3, square root of, 54, end square root
2
150
​
+3
54
​

Answer
Attempt 1 out of 5

Answer 1

To simplify the expression \( 2\sqrt{150} + 3\sqrt{54} \), we will begin by simplifying each square root.

### Step 1: Simplify \(\sqrt{150}\)
The number 150 can be factored as follows:
\[
150 = 25 \times 6 = 5^2 \times 6
\]
Taking the square root, we have:
\[
\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \cdot \sqrt{6} = 5\sqrt{6}
\]

### Step 2: Simplify \(\sqrt{54}\)
The number 54 can be factored as follows:
\[
54 = 9 \times 6 = 3^2 \times 6
\]
Taking the square root, we have:
\[
\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6}
\]

### Step 3: Substitute back into the expression
Now substitute back into the original expression:
\[
2\sqrt{150} + 3\sqrt{54} = 2(5\sqrt{6}) + 3(3\sqrt{6})
\]
This simplifies to:
\[
10\sqrt{6} + 9\sqrt{6}
\]

### Step 4: Combine like terms
Combine the two terms:
\[
10\sqrt{6} + 9\sqrt{6} = (10 + 9)\sqrt{6} = 19\sqrt{6}
\]

### Final Answer
Thus, the expression in simplest radical form is:
\[
\boxed{19\sqrt{6}}
\]