# How do you rationalize the denominator and simplify 30/sqrt18?

Mar 21, 2016

$5 \sqrt{2}$

#### Explanation:

To rationalise the denominator multiply numerator and denominator by $\sqrt{18}$
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Note : $\sqrt{a} \times \sqrt{a} = a \text{ eliminate the radical }$

example : $\sqrt{100} \times \sqrt{100} = 10 \times 10 = 100$

Also : $\sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a} b$
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$\Rightarrow \frac{30}{\sqrt{18}} \times \frac{\sqrt{18}}{\sqrt{18}} = \frac{30 \sqrt{18}}{18} = \frac{5 \sqrt{18}}{3}$

now $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}$

hence : $\frac{5 \sqrt{18}}{3} = \frac{5 \times 3 \sqrt{2}}{3} = \frac{5 \cancel{3} \sqrt{2}}{\cancel{3}}$

$\Rightarrow \frac{30}{\sqrt{18}} = 5 \sqrt{2}$