What is (sqrt(3)+1)/(sqrt(2-\sqrt{3))} ?

The solution to (sqrt(3)+1)/(sqrt(2-\sqrt{3))} is 3sqrt(3)sqrt(2-\sqrt{3)}+5sqrt(2-\sqrt{3)}

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simplify (sqrt(3)+1)/(sqrt(2-\sqrt{3))}

simplify

\frac{3 + 1}{2 - 3}

33 2 - 3 + 5 2 - 3

Decimal

5.27791 \dots

Solution steps

\frac{3 + 1}{2 - 3}

Multiply by the conjugate

\frac{2 - 3}{2 - 3}

= \frac{( 3 + 1 ) 2 - 3}{2 - 3 2 - 3}

2 - 3 2 - 3 = 2 - 3

= \frac{( 3 + 1 ) 2 - 3}{2 - 3}

Multiply by the conjugate

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

= \frac{( 3 + 1 ) 2 - 3 ( 2 + 3 )}{( 2 - 3 ) ( 2 + 3 )}

(3 + 1) 2 - 3 (2 + 3) = 33 2 - 3 + 5 2 - 3

(2 - 3) (2 + 3) = 1

= \frac{3 3 2 - 3 + 5 2 - 3}{1}

Apply rule

\frac{a}{1} = a

= 33 2 - 3 + 5 2 - 3

- \frac{1}{4 ( \frac{1}{4 x} )}

(1 + x)^{8}

- (x - 1)^{3}

\frac{m + 3}{m - 3} + \frac{m + 2}{m - 2}

\frac{448 u ^{3} y ^{3}}{900 u ^{2} y ^{11}}

What is (sqrt(3)+1)/(sqrt(2-\sqrt{3))} ?
The solution to (sqrt(3)+1)/(sqrt(2-\sqrt{3))} is 3sqrt(3)sqrt(2-\sqrt{3)}+5sqrt(2-\sqrt{3)}