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

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

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simplify (sqrt(2))/(sqrt(6)-2)

simplify

\frac{2}{6 - 2}

3 + 2

Decimal Notation

3.14626 \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) : 23 + 22

Expand

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

= \frac{2 3 + 2 2}{2}

Factor out common term

2

= \frac{2 ( 3 + 2 )}{2}

Cancel the common factor:

2

= 3 + 2

x y + 7 x + 4 y + 28

x^{4} + 6 x^{3} + 3 x + 140

\frac{4}{5} - \frac{1}{13}

2 x^{3} + 5 x^{2}

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