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

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

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

simplify

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

2 - 3

Decimal Notation

0.26794 \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 exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= (2 - 3)^{2}

Apply radical rule:

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

= 2 - 3

e^{- 8 l n (x)}

4 x^{2} y^{2}

e^{- 2 x} \cdot e^{x}

(2 - 3) (2 - 3)

(2 m^{5}) (4 m^{5})

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