Question

7 squareroot 150 + 6 squareroot 6

Answers

GPT-4o mini
To simplify the expression \( 7\sqrt{150} + 6\sqrt{6} \), we start by simplifying \( \sqrt{150} \).

The number \( 150 \) can be factored as:
\[
150 = 25 \times 6
\]
So, we can write:
\[
\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}
\]

Now, we substitute \( \sqrt{150} \) back into the original expression:
\[
7\sqrt{150} = 7 \times 5\sqrt{6} = 35\sqrt{6}
\]

Now, we can rewrite the entire expression:
\[
7\sqrt{150} + 6\sqrt{6} = 35\sqrt{6} + 6\sqrt{6}
\]

We can now combine the like terms:
\[
35\sqrt{6} + 6\sqrt{6} = (35 + 6)\sqrt{6} = 41\sqrt{6}
\]

Thus, the simplified form of the expression \( 7\sqrt{150} + 6\sqrt{6} \) is:
\[
\boxed{41\sqrt{6}}
\]