What is 2/(5-sqrt(23)) ?

The solution to 2/(5-sqrt(23)) is 5+sqrt(23)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/(5-sqrt(23))

simplify

\frac{2}{5 - 23}

5 + 23

Decimal Notation

9.79583 \dots

Solution steps

\frac{2}{5 - 23}

Multiply by the conjugate

\frac{5 + 23}{5 + 23}

= \frac{2 ( 5 + 23 )}{( 5 - 23 ) ( 5 + 23 )}

Expand

2 (5 + 23) : 10 + 223

Expand

(5 - 23) (5 + 23) : 2

= \frac{10 + 2 23}{2}

Factor out common term

2 : 2 (5 + 23)

= \frac{2 ( 5 + 23 )}{2}

Cancel the common factor:

2

= 5 + 23

π (2.5)^{2}

(u + 1)^{3}

lo g_{10} (10) x^{5}

\frac{28}{50}