Question
Answer
$$\dfrac{\sqrt{169}-120}{\sqrt{25}}=-\dfrac{107}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{169}-120}{\sqrt{25}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{169}-120}{\sqrt{25}}\frac{\sqrt{25}}{\sqrt{25}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{65-600}{25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-535}{25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{535}{25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}- \, \frac{ 535 : \color{orangered}{ 5 } }{ 25 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{107}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{25}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{169}-120\right) } \cdot \sqrt{25} = \color{blue}{ \sqrt{169}} \cdot \sqrt{25}\color{blue}{-120} \cdot \sqrt{25} = \\ = 65-600 $$ Simplify denominator. $$ \color{blue}{ \sqrt{25} } \cdot \sqrt{25} = 25 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place minus sign in front of the fraction. |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $. |
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