What is 6/(10-sqrt(2)) ?

The solution to 6/(10-sqrt(2)) is (3(10+sqrt(2)))/(49)

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Popular >

simplify 6/(10-sqrt(2))

simplify

\frac{6}{10 - 2}

\frac{3 ( 10 + 2 )}{49}

Decimal Notation

0.69882 \dots

Solution steps

\frac{6}{10 - 2}

Multiply by the conjugate

\frac{10 + 2}{10 + 2}

= \frac{6 ( 10 + 2 )}{( 10 - 2 ) ( 10 + 2 )}

Expand

6 (10 + 2) : 60 + 62

Expand

(10 - 2) (10 + 2) : 98

= \frac{60 + 6 2}{98}

Factor out common term

6 : 6 (10 + 2)

= \frac{6 ( 10 + 2 )}{98}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 3 ( 10 + 2 )}{98}

Factor the number:

98 = 2 \cdot 49

= \frac{2 \cdot 3 ( 10 + 2 )}{2 \cdot 49}

Cancel the common factor:

2

= \frac{3 ( 10 + 2 )}{49}

\frac{0.001 + 1 - 1}{0.001}

(2 m^{3} + 1)^{2} - 4 m^{6} - 4 m^{3}

i^{131} - i^{9} + 1

sec^{2} (x) (1 - sin^{2} (x))