Question
Answer
$$\dfrac{\sqrt{45}}{\sqrt{4}}+\dfrac{\sqrt{27}}{\sqrt{9}}=\dfrac{3\sqrt{5}+2\sqrt{3}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{45}}{\sqrt{4}}+\frac{\sqrt{27}}{\sqrt{9}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6\sqrt{5}}{4}+\frac{9\sqrt{3}}{9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{5}}{4}+\frac{\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{5}}{4}+\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6\sqrt{5}+4\sqrt{3}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{3\sqrt{5}+2\sqrt{3}}{2}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{45} } \cdot \sqrt{4} = 6 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{4} } \cdot \sqrt{4} = 4 $$Multiply in a numerator. $$ \color{blue}{ \sqrt{27} } \cdot \sqrt{9} = 9 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{9} } \cdot \sqrt{9} = 9 $$ |
| ② | Divide both numerator and denominator by 9. |
| ③ | Remove 1 from denominator. |
| ④ | $$ \frac{6\sqrt{5}}{4}+\sqrt{3}
= \frac{6\sqrt{5}}{4} \cdot \color{blue}{\frac{ 1 }{ 1}} + \sqrt{3} \cdot \color{blue}{\frac{ 4 }{ 4}}
= \frac{6\sqrt{5}+4\sqrt{3}}{4} $$ |
| ⑤ | Divide both numerator and denominator by 2. |
This page was created using
Simplify Radical Expression