How do you rationalize the denominator and simplify: $\frac{2}{5 - \sqrt{2}}$ $2 / (5 - sqrt 2)$ ?

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How do you rationalize the denominator and simplify: $\frac{2}{5 - \sqrt{2}}$ $2 / (5 - sqrt 2)$ ?

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Answer 1 · 2015-04-04T15:29:14

To rationalize, multiply the numerator and the denominator by the conjugate of 5- $\sqrt{2}$ $sqrt2$ . This is 5+ $\sqrt{2}$ $sqrt2$ .

Accordingly it is 2(5+ $\sqrt{2}$ $sqrt2$ )/(5- $\sqrt{2}$ $sqrt2$ )(5+ $\sqrt{2}$ $sqrt2$ )
= 2(5+ $\sqrt{2}$ $sqrt2$ )/(25-2)
= $\frac{2}{23}$ $2/23$ (5+ $\sqrt{2}$ $sqrt2$ )

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How do you rationalize the denominator and simplify: $\frac{2}{5 - \sqrt{2}}$ $2 / (5 - sqrt 2)$ ?

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