How do you rationalise the denominator in 3/sqrt3?

Sep 1, 2016

$\sqrt{3}$

Explanation:

Its is not good maths practice to leave a surd in the denominator, it's preferable in the numerator.

Note that: $\sqrt{{x}^{2}} = x \text{ and } x = \sqrt{x} \times \sqrt{x}$

$\frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

=$\frac{\cancel{3} \sqrt{3}}{\cancel{3}}$

=$\sqrt{3}$

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An alternative method:

$\frac{3}{\sqrt{3}} = \frac{\sqrt{3} \times \sqrt{3}}{\sqrt{3}}$

$\frac{\cancel{\sqrt{3}} \times \sqrt{3}}{\cancel{\sqrt{3}}}$

=$\sqrt{3}$