Question
Answer
$$\sqrt{\dfrac{4}{7}}=\dfrac{2}{7}\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{4}{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{7}\sqrt{28} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2}{7}\sqrt{7}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 4 }{ 7 } } = \frac{ \sqrt{ 4 } } {\sqrt{ 7 }}
= \frac{ \sqrt{ 4 } } {\sqrt{ 7 }} \cdot \frac{ \sqrt{ 7 } } {\sqrt{ 7 }} = \\
= \frac{ \sqrt{ 28 }} { 7 } = \frac{ 1 }{ 7 } \sqrt{ 28 } $$ |
| ② | $$ \frac{ 1 }{ 7 } \sqrt{ 28 } =
\frac{ 1 }{ 7 } \sqrt{ 2 ^2 \cdot 7 } =
\frac{ 1 }{ 7 } \sqrt{ 2 ^2 } \, \sqrt{ 7 } =
\frac{ 1 }{ 7 } \cdot 2 \sqrt{ 7 } =
\frac{ 2 }{ 7 } \sqrt{ 7 } $$ |
This page was created using
Simplify Radical Expression