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Rationalize denominator calculator
This calculator removes square roots from the denominator. The calculator rationalizes denominators containing one or two radical terms. For one radical term, the calculator multiplies the numerator and denominator by the square root, for two radical terms, it uses multiplication by the conjugate method. Additionally, the calculator shows all the steps with easy-to-understand explanations.
solution
$$\frac{9}{\sqrt{10}}=\frac{9\sqrt{10}}{10}$$explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 9 }{\sqrt{ 10 }} \times \frac{ \color{orangered}{\sqrt{ 10 }} }{ \color{orangered}{\sqrt{ 10 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9\sqrt{10}}{10}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 10 }}$. |
| ② | In denominator we have $ \sqrt{ 10 } \cdot \sqrt{ 10 } = 10 $. |
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Examples
ex 1:
$$\frac{1}{\sqrt{8}}$$
ex 2:
$$\frac{\sqrt{2} + 1}{\sqrt{2} -1}$$
ex 3:
$$\frac{3\sqrt{2} - 2\sqrt{3}}{2\sqrt{3} + 3\sqrt{2}}$$
ex 4:
$$\frac{1}{\sqrt{21} + \sqrt{7} + 2\sqrt{3} + 2}$$
ex 5:
$$\frac{\sqrt{3} + \sqrt{2} + 1}{\sqrt{3} - \sqrt{2} + 1}$$
ex 6:
$$\frac{11 - \sqrt{6}}{\sqrt{6} - 6}$$
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