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

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

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simplify (5-sqrt(5))/(2+sqrt(2))

simplify

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

\frac{10 - 5 2 - 2 5 + 10}{2}

Decimal Notation

0.80953 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(5 - 5) (2 - 2) : 10 - 52 - 25 + 10

Expand

(2 + 2) (2 - 2) : 2

= \frac{10 - 5 2 - 2 5 + 10}{2}

\frac{x \cdot x ^{3}}{x ^{4}}

x y^{0}

\frac{3}{8} + \frac{4}{5}

16 \frac{7}{14} - 12 \frac{8}{21}

(- a)^{3}

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