Question

Which expression is equivalent to title="18x\sqrt{14x^8}/6\sqrt{7x^4" alt="18x\sqrt{14x^8}/6\sqrt{7x^4" align="absmiddle" class="latex-formula"> if $x\neq 0$
a. $12x^4\sqrt{2}$
b. $3x^4\sqrt{2}$
c. $3x^4\sqrt{7}$
d. $3x\sqrt{2}$

Answer 1

The equivalent expression is $3x^4\sqrt{2}$ . Option B

How to determine the expression

Given the expression

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

Divide the multipliers, we have

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

Let factorize the numerator in square root

= $\frac{3x \sqrt{7x^4 * 2x^4} }{7x^4}$

Eliminate the like factor in both the numerator and denominator

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

Let's bring forth the 'x' factor, we have

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

Thus, the equivalent expression $3x^4\sqrt{2}$ . Option B

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