Change the radical to simplest radical form. $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$
A) $- \frac { \sqrt { 21 } } { 49 }$
B) $\frac { 21 } { 21 } \sqrt { 12 }$
C) $4 \sqrt { 7 }$
D) $- \frac { 4 } { 49 } \sqrt { 7 }$
E) $- \frac { 2 } { 7 } \frac { \sqrt { 4 } } { \sqrt { 7 } }$

Question

Quizplus · Accepted Answer

First, simplify $\sqrt{12}$ to $2\sqrt{3}$ and $\sqrt{21}$ as is. Then, divide both numerator and denominator by their GCD, which is 3, to get $-\frac{2\sqrt{3}}{7\sqrt{7}}$. Multiplying numerator and denominator by $\sqrt{7}$ to rationalize the denominator gives $-\frac{2\sqrt{21}}{49}$, which simplifies to $-\frac{4}{49}\sqrt{7}$.

Change the Radical to Simplest Radical Form −6122121- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }−2121​612​​

Change the Radical to Simplest Radical Form $- \frac { 6 \sqrt { 12 } } { 21 \sqrt { 21 } }$