Question

select the correct answer.
which expression is equivalent to $18x^{2}\sqrt{14x^{8}} \div 6\sqrt{7x^{4}}$, if $x \
eq 0$
a. $12x^{4}\sqrt{2}$
b. $3x^{4}\sqrt{2}$
c. $3x^{4}\sqrt{7}$
d. $3x\sqrt{2}$

Explanation:

Step1: Split into rational/radical parts

$\frac{18x^2}{6} \times \frac{\sqrt{14x^8}}{\sqrt{7x^4}}$

Step2: Simplify rational coefficients

$3x^2 \times \frac{\sqrt{14x^8}}{\sqrt{7x^4}}$

Step3: Combine radicals via quotient rule

$3x^2 \times \sqrt{\frac{14x^8}{7x^4}}$

Step4: Simplify radical argument

$3x^2 \times \sqrt{2x^4}$

Step5: Simplify the radical term

$3x^2 \times x^2\sqrt{2}$

Step6: Multiply like variable terms

$3x^{2+2}\sqrt{2} = 3x^4\sqrt{2}$

Answer:

B. $3x^4\sqrt{2}$