What is 3/(3-2sqrt(2)) ?

The solution to 3/(3-2sqrt(2)) is 9+6sqrt(2)

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simplify 3/(3-2sqrt(2))

simplify

\frac{3}{3 - 2 2}

9 + 62

Decimal Notation

17.48528 \dots

Solution steps

\frac{3}{3 - 2 2}

Multiply by the conjugate

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

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

Expand

3 (3 + 22) : 9 + 62

Expand

(3 - 22) (3 + 22) : 1

= \frac{9 + 6 2}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 9 + 62

- \frac{7}{28}

2 n^{2} + 7 n + 5

45 x^{2} y^{2} z^{2} - 38 y^{5} z^{3}

\frac{4}{13}

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