What is 3/(3+sqrt(6)) ?

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

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simplify 3/(3+sqrt(6))

simplify

\frac{3}{3 + 6}

3 - 6

Decimal Notation

0.55051 \dots

Solution steps

\frac{3}{3 + 6}

Multiply by the conjugate

\frac{3 - 6}{3 - 6}

= \frac{3 ( 3 - 6 )}{( 3 + 6 ) ( 3 - 6 )}

Expand

3 (3 - 6) : 9 - 36

Expand

(3 + 6) (3 - 6) : 3

= \frac{9 - 3 6}{3}

Factor out common term

3 : 3 (3 - 6)

= \frac{3 ( 3 - 6 )}{3}

Cancel the common factor:

3

= 3 - 6

5 \times 5 \times 5

\frac{x ^{0}}{x ^{5}}

\frac{4}{5} + 5

1 \frac{3}{5} \div 5 \frac{1}{3}

\frac{\frac{1}{4}}{\frac{1}{8}}