Question
Answer
$$\sqrt{245}^3=1715\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{245}^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(7\sqrt{5})^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1715\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{245} =
\sqrt{ 7 ^2 \cdot 5 } =
\sqrt{ 7 ^2 } \, \sqrt{ 5 } =
7 \sqrt{ 5 }$$ |
| ② | $$ (7\sqrt{5})^3 =
7^{ 3 } \cdot \sqrt{5} ^ { 3 } =
7^{ 3 } \sqrt{5} ^2 \cdot \sqrt{5} =
7^{ 3 } \lvert 5 \rvert \cdot \sqrt{5} =
1715\sqrt{5} $$ |
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