Question

simplify (3sqrt{32x^{4}z}). assume (x) and (z) are nonnegative.

(48x^{2}sqrt{2z})
(12sqrt{x^{2}z})
(12x^{2}sqrt{2z})
(48x^{2}sqrt{x^{2}z})

Explanation:

Step1: Factor 32

$32 = 16\times2$, so $3\sqrt{32x^{4}z}=3\sqrt{16\times2\times x^{4}z}$

Step2: Use square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$3\sqrt{16\times2\times x^{4}z}=3\sqrt{16}\cdot\sqrt{2}\cdot\sqrt{x^{4}}\cdot\sqrt{z}$

Step3: Calculate square - roots

Since $\sqrt{16} = 4$ and $\sqrt{x^{4}}=x^{2}$, we have $3\times4\times\sqrt{2}\times x^{2}\times\sqrt{z}=12x^{2}\sqrt{2z}$

Answer:

C. $12x^{2}\sqrt{2z}$