Question

algebra q1 review (radicals)
simplify.
√24·√8

Explanation:

Step1: Prime - factorize numbers inside radicals

$\sqrt{24}=\sqrt{2\times2\times2\times3}=2\sqrt{6}$ and $\sqrt{8}=\sqrt{2\times2\times2}=2\sqrt{2}$

Step2: Multiply the simplified radicals

$2\sqrt{6}\times2\sqrt{2}=(2\times2)\times\sqrt{6\times2}=4\sqrt{12}$

Step3: Simplify the resulting radical

$\sqrt{12}=\sqrt{2\times2\times3}=2\sqrt{3}$, so $4\sqrt{12}=4\times2\sqrt{3}=8\sqrt{3}$

Answer:

$8\sqrt{3}$