To simplify the product of \( \sqrt{6} \times 2\sqrt{18} \), we can first rewrite the expression:
\[ \sqrt{6} \times 2\sqrt{18} = 2\sqrt{6} \times \sqrt{18} \]
Next, we can combine the square roots:
\[ 2\sqrt{6 \times 18} \]
Now, we need to calculate \( 6 \times 18 \):
\[ 6 \times 18 = 108 \]
Thus, we have:
\[ 2\sqrt{108} \]
Next, we simplify \( \sqrt{108} \). First, we factor \( 108 \):
\[ 108 = 36 \times 3 \] So, we can write:
\[ \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3} \]
Now, substituting this back into our expression gives us:
\[ 2\sqrt{108} = 2 \times 6\sqrt{3} = 12\sqrt{3} \]
Thus, the product of \( \sqrt{6} \times 2\sqrt{18} \) in simplest radical form is:
\[ \boxed{12\sqrt{3}} \]
1 answer