What is (2+sqrt(2))/(sqrt(3)+\sqrt{6)} ?

The solution to (2+sqrt(2))/(sqrt(3)+\sqrt{6)} is (sqrt(2))/(sqrt(3))

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simplify (2+sqrt(2))/(sqrt(3)+\sqrt{6)}

simplify

\frac{2 + 2}{3 + 6}

\frac{2}{3}

Decimal Notation

0.81649 \dots

Solution steps

\frac{2 + 2}{3 + 6}

Multiply by the conjugate

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

= \frac{( 2 + 2 ) ( 3 - 6 )}{( 3 + 6 ) ( 3 - 6 )}

Expand

(2 + 2) (3 - 6) : - 6

Expand

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

= \frac{- 6}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6}{3}

Factor

6 : 32

= \frac{3 2}{3}

Apply radical rule:

a = a a

3 = 33

= \frac{3 2}{3 3}

Cancel the common factor:

3

= \frac{2}{3}

\frac{( 2 x + 7 ) ^{5} + ( x + 4 ) ^{2} - 7 x}{x + 3}

\frac{sec ( x )}{cos ( x )}

(\frac{1}{3})^{13} \cdot 3^{13}

\frac{30}{14} \div \frac{60}{35}

sec^{2} (x) + tan^{2} (x)

What is (2+sqrt(2))/(sqrt(3)+\sqrt{6)} ?
The solution to (2+sqrt(2))/(sqrt(3)+\sqrt{6)} is (sqrt(2))/(sqrt(3))