What is (sqrt(2))/(6+sqrt(2)) ?

The solution to (sqrt(2))/(6+sqrt(2)) is (3sqrt(2)-1)/(17)

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simplify (sqrt(2))/(6+sqrt(2))

simplify

\frac{2}{6 + 2}

\frac{3 2 - 1}{17}

Decimal Notation

0.19074 \dots

Solution steps

\frac{2}{6 + 2}

Multiply by the conjugate

\frac{6 - 2}{6 - 2}

= \frac{2 ( 6 - 2 )}{( 6 + 2 ) ( 6 - 2 )}

Expand

2 (6 - 2) : 62 - 2

Expand

(6 + 2) (6 - 2) : 34

= \frac{6 2 - 2}{34}

Factor out common term

2 : 2 (32 - 1)

= \frac{2 ( 3 2 - 1 )}{34}

Factor the number:

34 = 2 \cdot 17

= \frac{2 ( 3 2 - 1 )}{2 \cdot 17}

Cancel the common factor:

2

= \frac{3 2 - 1}{17}

5 x + 10 = 5 x + 20

7^{- \frac{1}{6}}

5 - \frac{1}{4} x^{2} = 2 - \frac{1}{8} x^{2}

x + 5 > 13

8 m^{2} - 12 mn

What is (sqrt(2))/(6+sqrt(2)) ?
The solution to (sqrt(2))/(6+sqrt(2)) is (3sqrt(2)-1)/(17)