What is 2/(sqrt(3)+1) ?

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

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simplify 2/(sqrt(3)+1)

simplify

\frac{2}{3 + 1}

3 - 1

Decimal Notation

0.73205 \dots

Solution steps

\frac{2}{3 + 1}

Multiply by the conjugate

\frac{3 - 1}{3 - 1}

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

Expand

2 (3 - 1) : 23 - 2

Expand

(3 + 1) (3 - 1) : 2

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

Factor out common term

2 : 2 (3 - 1)

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

Cancel the common factor:

2

= 3 - 1

441 - (4 0.5)^{2}

3.98

2 x y (- x^{3} - y^{4} - x^{5} y^{5})

1 0^{l o g_{10} (14)}