What is (sqrt(8))/(5-sqrt(3)) ?

The solution to (sqrt(8))/(5-sqrt(3)) is (5sqrt(2)+sqrt(6))/(11)

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simplify (sqrt(8))/(5-sqrt(3))

simplify

\frac{8}{5 - 3}

\frac{5 2 + 6}{11}

Decimal Notation

0.86550 \dots

Solution steps

\frac{8}{5 - 3}

Multiply by the conjugate

\frac{5 + 3}{5 + 3}

= \frac{8 ( 5 + 3 )}{( 5 - 3 ) ( 5 + 3 )}

Expand

8 (5 + 3) : 102 + 26

Expand

(5 - 3) (5 + 3) : 22

= \frac{10 2 + 2 6}{22}

Factor out common term

2 : 2 (52 + 6)

= \frac{2 ( 5 2 + 6 )}{22}

Factor the number:

22 = 2 \cdot 11

= \frac{2 ( 5 2 + 6 )}{2 \cdot 11}

Cancel the common factor:

2

= \frac{5 2 + 6}{11}

\frac{1}{6} + \frac{4}{9}

(x - 5) (x^{2} + 4 x - 2)

(\frac{sin ( x )}{cos ( x )})^{2}

(x + 2 x)^{2}

\frac{1}{2} + \frac{1}{2}

What is (sqrt(8))/(5-sqrt(3)) ?
The solution to (sqrt(8))/(5-sqrt(3)) is (5sqrt(2)+sqrt(6))/(11)