# Rationalize the denominator. displaystylefrac{sqrt{{40}}}{sqrt{{56}}}

Question
Rationalize the denominator.
$$\displaystyle\frac{\sqrt{{40}}}{\sqrt{{56}}}$$

2021-01-11
Step 1
We write them under one radical. Then recue $$\displaystyle\frac{40}{{56}}$$ by 8.
$$\displaystyle=\frac{\sqrt{{40}}}{\sqrt{{56}}}$$
$$\displaystyle=\sqrt{{\frac{40}{{56}}}}$$
$$\displaystyle=\sqrt{{\frac{{{40}\div{8}}}{{{56}\div{8}}}}}$$
$$\displaystyle=\sqrt{{\frac{5}{{7}}}}$$
Step 2
Separate the radicals. And multiply numerator and denominator by $$\sqrt{7}$$
$$\displaystyle\sqrt{{\frac{5}{{7}}}}$$
$$\displaystyle=\frac{\sqrt{{5}}}{\sqrt{{7}}}$$
$$\displaystyle=\frac{{\sqrt{{5}}\times\sqrt{{7}}}}{{\sqrt{{7}}\times\sqrt{{7}}}}$$
$$\displaystyle==\frac{\sqrt{{{35}}}}{{7}}$$
Answer: $$\displaystyle\frac{\sqrt{{{35}}}}{{7}}$$

### Relevant Questions

To rationalize:
Each numerator. Assume that variables represent positive real numbers.
Given: An expression : $$\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}.$$
To calculate:
To rationalize the denominator of the expression $$\displaystyle{\frac{{\sqrt{{{5}}}\ -\ \sqrt{{{2}}}}}{{\sqrt{{{5}}}\ +\ \sqrt{{{2}}}}}}.$$
Find the rationalize the denominator of $$\frac{-4}{\sqrt[3]{5x}}$$
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To calculate:
The expression $$\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}$$ with positive exponent.
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To multiply:
The given expression. Then simplify if possible. Assume that all variables represent positive real numbers.
Given:
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$$\displaystyle{\sqrt[{{4}}]{{{c}{d}^{2}}}}\times{\sqrt[{{3}}]{{{c}^{2}{d}}}}.$$
$$\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}$$
An expression: $$\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}.$$