Question

select the correct answer.
which expression is equivalent to $sqrt3{54x} + 3sqrt3{2x}$, if $x \
eq 0$
a. $6sqrt3{2x}$
b. $3sqrt3{56x}$
c. $4sqrt3{56x}$
d. $5sqrt3{5x}$

Explanation:

Step1: Simplify \(\sqrt[3]{54x}\)

Factor 54: \(54 = 27\times2\), so \(\sqrt[3]{54x}=\sqrt[3]{27\times2x}\). Since \(\sqrt[3]{27}=3\), this becomes \(3\sqrt[3]{2x}\).

Step2: Add the two terms

Now we have \(3\sqrt[3]{2x}+3\sqrt[3]{2x}\). Combine like terms: \((3 + 3)\sqrt[3]{2x}=6\sqrt[3]{2x}\).

Answer:

A. \(6\sqrt[3]{2x}\)