What is 2/(5+sqrt(3)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/(5+sqrt(3))

simplify

\frac{2}{5 + 3}

\frac{5 - 3}{11}

Decimal Notation

0.29708 \dots

Solution steps

\frac{2}{5 + 3}

Multiply by the conjugate

\frac{5 - 3}{5 - 3}

= \frac{2 ( 5 - 3 )}{( 5 + 3 ) ( 5 - 3 )}

Expand

2 (5 - 3) : 10 - 23

Expand

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

= \frac{10 - 2 3}{22}

Factor out common term

2 : 2 (5 - 3)

= \frac{2 ( 5 - 3 )}{22}

Factor the number:

22 = 2 \cdot 11

= \frac{2 ( 5 - 3 )}{2 \cdot 11}

Cancel the common factor:

2

= \frac{5 - 3}{11}

\frac{e ^{i w} - e ^{- i w}}{e ^{i w} + e ^{- i w}}

(5 h - 3)^{2}

\frac{6 x - 18}{x ^{2} - 4} \cdot \frac{x ^{2} + 5 x + 6}{x ^{2} - 9}

- 5 + \frac{1}{3}

(3 x^{2} - 5) (3 x^{2} + 5) - x^{2} (3 x - 1)^{2}