What is 2/(8+sqrt(5)) ?

The solution to 2/(8+sqrt(5)) is (16-2sqrt(5))/(59)

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simplify 2/(8+sqrt(5))

simplify

\frac{2}{8 + 5}

\frac{16 - 2 5}{59}

Decimal Notation

0.19538 \dots

Solution steps

\frac{2}{8 + 5}

Multiply by the conjugate

\frac{8 - 5}{8 - 5}

= \frac{2 ( 8 - 5 )}{( 8 + 5 ) ( 8 - 5 )}

Expand

2 (8 - 5) : 16 - 25

Expand

(8 + 5) (8 - 5) : 59

= \frac{16 - 2 5}{59}

sin (x) cos (x) + cos (x) sin (x)

- \frac{30}{4}

- \frac{30}{5}

425 + 34

\frac{5. 1 ^{2} - 25}{5.1 - 5}