What is 2/(sqrt(2-\sqrt{2))} ?

The solution to 2/(sqrt(2-\sqrt{2))} is 2sqrt(2-\sqrt{2)}+sqrt(2)sqrt(2-\sqrt{2)}

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simplify 2/(sqrt(2-\sqrt{2))}

simplify

\frac{2}{2 - 2}

2 2 - 2 + 2 2 - 2

Decimal Notation

2.61312 \dots

Solution steps

\frac{2}{2 - 2}

Multiply by the conjugate

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

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

2 - 2 2 - 2 = 2 - 2

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

Factor

2 - 2 : 2 (2 - 1)

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

Cancel

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

= \frac{2 2 - 2}{2 - 1}

Multiply by the conjugate

\frac{2 + 1}{2 + 1}

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

2 2 - 2 (2 + 1) = 2 2 - 2 + 2 2 - 2

(2 - 1) (2 + 1) = 1

= \frac{2 2 - 2 + 2 2 - 2}{1}

Apply rule

\frac{a}{1} = a

= 2 2 - 2 + 2 2 - 2

(1 + 2 x^{2})^{2}

15 - (- 5)

- 9 (\frac{- 8}{9})

3^{- \frac{5}{6}}

+ 64 x^{2} y^{2} - 1

What is 2/(sqrt(2-\sqrt{2))} ?
The solution to 2/(sqrt(2-\sqrt{2))} is 2sqrt(2-\sqrt{2)}+sqrt(2)sqrt(2-\sqrt{2)}