Solve the equation by using the Square Root Property. $9 u ^ { 2 } + 30 = 0$
A) $u = \pm \sqrt { 30 }$
B) $u = \pm \frac { \sqrt { 30 } } { 9 } i$
C) $u = \pm \frac { \sqrt { 30 } } { 3 }$
D) $u = \pm \frac { \sqrt { 30 } } { 9 }$
E) $u = \pm \frac { \sqrt { 30 } } { 3 } i$

Question

Quizplus · Accepted Answer

To use the Square Root Property, we need to isolate the variable, which means we need to move the constant term to the other side of the equation: 
\begin{align*} 
9u^2 &= -30 \
u^2 &= -\frac{30}{9} \
u^2 &= -\frac{10}{3}
\end{align*}
However, since we cannot take the square root of a negative number in the real number system, we have to use imaginary numbers. The square root of $-1$ is denoted by $i$, so we have:
\begin{align*}
u &= \pm \sqrt{-\frac{10}{3}} \
&= \pm \sqrt{\frac{-10}{3}} \
&= \pm \sqrt{\frac{-10}{3} \cdot \frac{3}{3}} \
&= \pm \sqrt{\frac{-30}{9}} \
&= \pm \frac{\sqrt{30}}{\sqrt{9}} \cdot \sqrt{-1} \
&= \pm \frac{\sqrt{30}}{3} i \
\end{align*}
Therefore, the answer is E.

Solve the Equation by Using the Square Root Property 9u2+30=09 u ^ { 2 } + 30 = 09u2+30=0

Solve the Equation by Using the Square Root Property $9 u ^ { 2 } + 30 = 0$