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

The solution to (sqrt(2-\sqrt{2)})/(sqrt(2+\sqrt{2))} is sqrt(2)-1

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

simplify

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

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

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

Apply radical rule:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

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

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

Cancel

\frac{2 - 2}{2 + 2} : 3 - 22

= 3 - 22

= 2 - 22 + 1

= (2)^{2} - 22 + (1)^{2}

1 = 1

= (2)^{2} - 22 + 1^{2}

22 \cdot 1 = 22

= (2)^{2} - 22 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(2)^{2} - 22 \cdot 1 + 1^{2} = (2 - 1)^{2}

= (2 - 1)^{2}

Apply radical rule:

(2 - 1)^{2} = 2 - 1

= 2 - 1

e^{- \frac{8}{5}}

- x^{2} y^{2} (x^{4} - y^{4} + z^{2} - x^{2} y^{2} + y^{2} z^{2})

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

(481) (4 - 64)

(4 x^{3}) (2 x^{4})

What is (sqrt(2-\sqrt{2)})/(sqrt(2+\sqrt{2))} ?
The solution to (sqrt(2-\sqrt{2)})/(sqrt(2+\sqrt{2))} is sqrt(2)-1