Question
\sqrt{6\cdot\sqrt{12}} simplified
Answers
GPT 3.5
First, we simplify the expression under the radical.
$6\cdot\sqrt{12} = 6\cdot\sqrt{4\cdot3} = 6\cdot2\cdot\sqrt{3} = 12\sqrt{3}$
Now, we can simplify the entire expression:
$\sqrt{6\cdot\sqrt{12}} = \sqrt{12\sqrt{3}} = \sqrt{(2^2)\cdot\sqrt{3}} = \sqrt{2^2}\sqrt{\sqrt{3}} = 2\sqrt[4]{3} = \boxed{2\sqrt[4]{3}}$
$6\cdot\sqrt{12} = 6\cdot\sqrt{4\cdot3} = 6\cdot2\cdot\sqrt{3} = 12\sqrt{3}$
Now, we can simplify the entire expression:
$\sqrt{6\cdot\sqrt{12}} = \sqrt{12\sqrt{3}} = \sqrt{(2^2)\cdot\sqrt{3}} = \sqrt{2^2}\sqrt{\sqrt{3}} = 2\sqrt[4]{3} = \boxed{2\sqrt[4]{3}}$