Exercises: Making Denominators Rational

Make the denominator rational:

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$\frac{\sqrt{2} - \sqrt{125}}{\sqrt{5}}$	$=$	$\frac{\sqrt{2} - \sqrt{125}}{\sqrt{5}}$
	↓	Expand the fraction by $\sqrt{5}$ .
	$=$	$\frac{(\sqrt{2} - \sqrt{125}) \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}$
	↓	Multiply.
	$=$	$\frac{\sqrt{10} - \sqrt{625}}{5}$
	↓	Take the square root.
	$=$	$\frac{\sqrt{10} - 25}{5}$
	$=$	$\frac{\sqrt{10}}{5} - 5$