What is 1/(4-2sqrt(2)) ?

The solution to 1/(4-2sqrt(2)) is (2+sqrt(2))/4

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simplify 1/(4-2sqrt(2))

simplify

\frac{1}{4 - 2 2}

\frac{2 + 2}{4}

Decimal Notation

0.85355 \dots

Solution steps

\frac{1}{4 - 2 2}

Multiply by the conjugate

\frac{4 + 2 2}{4 + 2 2}

= \frac{1 \cdot ( 4 + 2 2 )}{( 4 - 2 2 ) ( 4 + 2 2 )}

1 \cdot (4 + 22) = 4 + 22

(4 - 22) (4 + 22) = 8

= \frac{4 + 2 2}{8}

Factor

4 + 22 : 2 (2 + 2)

= \frac{2 ( 2 + 2 )}{8}

Cancel the common factor:

2

= \frac{2 + 2}{4}

- 4 x + 3 y + x - 2 z + 2 y

(\frac{3}{6})^{2}

12 \cdot y^{3} \cdot 6 y

- 3^{8}