Question

simplify
$4\sqrt{24} - \sqrt{150}$
$\circ \sqrt{6}$
$\circ 3\sqrt{6}$
$\circ -3\sqrt{6}$
$\circ 13\sqrt{6}$

Explanation:

Step1: Simplify each square root

Simplify \( \sqrt{24} \) and \( \sqrt{150} \) by factoring out perfect squares.
\( \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \)
\( \sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6} \)

Step2: Substitute back into the expression

Substitute the simplified square roots into \( 4\sqrt{24} - \sqrt{150} \).
\( 4\sqrt{24} = 4 \times 2\sqrt{6} = 8\sqrt{6} \)
So the expression becomes \( 8\sqrt{6} - 5\sqrt{6} \).

Step3: Combine like terms

Subtract the coefficients of \( \sqrt{6} \).
\( 8\sqrt{6} - 5\sqrt{6} = (8 - 5)\sqrt{6} = 3\sqrt{6} \)

Answer:

B. \( 3\sqrt{6} \)