What is 1/(5+sqrt(2)) ?

The solution to 1/(5+sqrt(2)) is (5-sqrt(2))/(23)

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simplify 1/(5+sqrt(2))

simplify

\frac{1}{5 + 2}

\frac{5 - 2}{23}

Solution steps

\frac{1}{5 + 2}

Multiply by the conjugate

\frac{5 - 2}{5 - 2}

= \frac{1 \cdot ( 5 - 2 )}{( 5 + 2 ) ( 5 - 2 )}

1 \cdot (5 - 2) = 5 - 2

(5 + 2) (5 - 2) = 23

= \frac{5 - 2}{23}

3 \cdot 3 \cdot 3 \cdot 3 \cdot 3

- \frac{1}{2} \times (- 1)

\frac{1 + 2}{2}

2 x^{2} \times 3 x

2 x^{5} - 33 x^{4} + 96 x^{3} + 304 x^{2} - 326 x + 77