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

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

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

simplify

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

3 + 2

Decimal Notation

3.73205 \dots

Solution steps

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

Apply radical rule:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

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

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

Cancel

\frac{2 + 3}{2 - 3} : 7 + 43

= 7 + 43

= 3 + 43 + 4

= (3)^{2} + 43 + (4)^{2}

4 = 2

= (3)^{2} + 43 + 2^{2}

23 \cdot 2 = 43

= (3)^{2} + 23 \cdot 2 + 2^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(3)^{2} + 23 \cdot 2 + 2^{2} = (3 + 2)^{2}

= (3 + 2)^{2}

Apply radical rule:

(3 + 2)^{2} = 3 + 2

= 3 + 2

3 n^{- 6} \cdot 5 e \cdot 3 e^{4} \cdot (- 2) n^{3}

3 e^{- l n (5)}

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