Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }$
A) $4 x \sqrt [ 3 ] { 7 }$
B) $4 \sqrt [ 3 ] { 7 x }$
C) $\sqrt [ 3 ] { 10 x }$
D) $4 + \sqrt [ 3 ] { 7 x }$
E) $\sqrt [ 3 ] { 7 x }$

Question

Quizplus · Accepted Answer

First, factor 189x as 27x*7, where 27 is a perfect cube. Then, $\sqrt[3]{189x} = \sqrt[3]{27x*7} = 3\sqrt[3]{7x}$. Adding this to $\sqrt[3]{7x}$ gives $3\sqrt[3]{7x} + \sqrt[3]{7x} = 4\sqrt[3]{7x}$.

Simplify by Combining Like Radicals 189x3+7x3\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }3189x​+37x​

Simplify by Combining Like Radicals $\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }$