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

The solution to 2/(5+sqrt(2)) is (10-2sqrt(2))/(23)

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simplify 2/(5+sqrt(2))

simplify

\frac{2}{5 + 2}

\frac{10 - 2 2}{23}

Decimal Notation

0.31180 \dots

Solution steps

\frac{2}{5 + 2}

Multiply by the conjugate

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

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

Expand

2 (5 - 2) : 10 - 22

Expand

(5 + 2) (5 - 2) : 23

= \frac{10 - 2 2}{23}

(m^{5} + 5 n^{4})^{2}

(x - 5) (x^{2} - 1)

80 x^{2}

25 y^{2} - 9

4 m^{2} n^{2} - 4 m n^{3}