Question
Answer
$$\sqrt{\dfrac{9}{10}}=\dfrac{3}{10}\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{9}{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{10}\sqrt{90} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{10}\sqrt{10}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 9 }{ 10 } } = \frac{ \sqrt{ 9 } } {\sqrt{ 10 }}
= \frac{ \sqrt{ 9 } } {\sqrt{ 10 }} \cdot \frac{ \sqrt{ 10 } } {\sqrt{ 10 }} = \\
= \frac{ \sqrt{ 90 }} { 10 } = \frac{ 1 }{ 10 } \sqrt{ 90 } $$ |
| ② | $$ \frac{ 1 }{ 10 } \sqrt{ 90 } =
\frac{ 1 }{ 10 } \sqrt{ 3 ^2 \cdot 10 } =
\frac{ 1 }{ 10 } \sqrt{ 3 ^2 } \, \sqrt{ 10 } =
\frac{ 1 }{ 10 } \cdot 3 \sqrt{ 10 } =
\frac{ 3 }{ 10 } \sqrt{ 10 } $$ |
This page was created using
Simplify Radical Expression