Question

simplify the expression. assume all variables represent positive real numbers. (sqrt3{24}) select the correct choice below and fill in any answer boxes in your choice. a. (sqrt3{24}=) (type an exact answer using radicals as needed.) b. the root is not a real number.

Explanation:

Step1: Prime - factorize 24

$24=2\times2\times2\times3 = 2^{3}\times3$

Step2: Apply cube - root property $\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}$

$\sqrt[3]{24}=\sqrt[3]{2^{3}\times3}=\sqrt[3]{2^{3}}\times\sqrt[3]{3}$

Step3: Simplify $\sqrt[3]{2^{3}}$

$\sqrt[3]{2^{3}} = 2$, so $\sqrt[3]{24}=2\sqrt[3]{3}$

Answer:

A. $\sqrt[3]{24}=2\sqrt[3]{3}$