Question
Answer
$$\dfrac{128}{\sqrt{63}\cdot\sqrt{2}}=\dfrac{64\sqrt{14}}{21}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{128}{\sqrt{63}\cdot\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{128}{\sqrt{63}\cdot\sqrt{2}}\frac{\sqrt{126}}{\sqrt{126}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{384\sqrt{14}}{126} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 384 \sqrt{ 14 } : \color{blue}{ 6 } } { 126 : \color{blue}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{64\sqrt{14}}{21}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{126}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 128 } \cdot \sqrt{126} = 384 \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ \sqrt{126} } \cdot \sqrt{126} = 126 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 6 } $. |
This page was created using
Rationalize Denominator Calculator