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

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

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

simplify

\frac{1}{2 - 3}

(2 + 3) 2 - 3

Decimal Notation

1.93185 \dots

Solution steps

\frac{1}{2 - 3}

Multiply by the conjugate

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

= \frac{1 \cdot 2 - 3}{2 - 3 2 - 3}

1 \cdot 2 - 3 = 2 - 3

2 - 3 2 - 3 = 2 - 3

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

Multiply by the conjugate

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

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

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

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

Apply rule

\frac{a}{1} = a

= (2 + 3) 2 - 3

\frac{7}{12} - \frac{5}{12}

40 (x + 2)^{2} - 18 (x + 2) - 7

x^{2} + 1 2^{2} = 1 5^{2}

\frac{5}{3} - 4

\frac{6}{9} \cdot 15

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