Question
Answer
$$\sqrt{\dfrac{7}{8}}=\dfrac{1}{4}\sqrt{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{7}{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{8}\sqrt{56} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{4}\sqrt{14}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 7 }{ 8 } } = \frac{ \sqrt{ 7 } } {\sqrt{ 8 }}
= \frac{ \sqrt{ 7 } } {\sqrt{ 8 }} \cdot \frac{ \sqrt{ 8 } } {\sqrt{ 8 }} = \\
= \frac{ \sqrt{ 56 }} { 8 } = \frac{ 1 }{ 8 } \sqrt{ 56 } $$ |
| ② | $$ \frac{ 1 }{ 8 } \sqrt{ 56 } =
\frac{ 1 }{ 8 } \sqrt{ 2 ^2 \cdot 14 } =
\frac{ 1 }{ 8 } \sqrt{ 2 ^2 } \, \sqrt{ 14 } =
\frac{ 1 }{ 8 } \cdot 2 \sqrt{ 14 } =
\frac{ 1 }{ 4 } \sqrt{ 14 } $$ |
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