How do you rationalize the denominator and simplify 4/sqrt2?

Jul 24, 2016

$2 \sqrt{2}$

Explanation:

Multiply by 1 but in the form of $1 = \frac{\sqrt{2}}{\sqrt{2}}$

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$\textcolor{b l u e}{\text{Comment}}$

Multiplying by 1 does not change the inherent value.
So multiplying by $1 = \frac{\sqrt{2}}{\sqrt{2}}$ changes the way it looks without changing its inherent value.
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$\frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} \text{ " =" } \frac{{\cancel{4}}^{2} \sqrt{2}}{{\cancel{2}}^{1}}$

$= 2 \sqrt{2}$