Use the quotient rule and the product rule to simplify each radical.
-$\sqrt { \frac { 1445 } { 9 } }$
A) $\sqrt { \frac { 1445 } { 9 } }$
B) $\frac { 17 \sqrt { 5 } } { 3 }$
C) $\frac { 289 \sqrt { 5 } } { 9 }$
D) $\frac { \sqrt { 1445 } } { 3 }$

Question

Quizplus · Accepted Answer

First, simplify the fraction under the radical: $1445 / 9 = 161$. The square root of 161 can be simplified to $\sqrt{161} = \sqrt{5 \times 5 \times 5} = 5\sqrt{5}$. However, the correct simplification of $\sqrt{1445/9}$ is actually $\sqrt{160.555...\}$, which was incorrectly simplified in the explanation. The correct approach is to simplify $\sqrt{1445/9}$ directly: $1445 = 5 \times 289 = 5 \times 17^2$, so $\sqrt{1445/9} = \sqrt{5 \times 17^2 / 3^2} = 17\sqrt{5}/3$, making option B correct.

Use the Quotient Rule and the Product Rule to Simplify 14459\sqrt { \frac { 1445 } { 9 } }91445​​

Use the Quotient Rule and the Product Rule to Simplify $\sqrt { \frac { 1445 } { 9 } }$