What is 2/(7-sqrt(5)) ?

The solution to 2/(7-sqrt(5)) is (7+sqrt(5))/(22)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/(7-sqrt(5))

simplify

\frac{2}{7 - 5}

\frac{7 + 5}{22}

Decimal Notation

0.41982 \dots

Solution steps

\frac{2}{7 - 5}

Multiply by the conjugate

\frac{7 + 5}{7 + 5}

= \frac{2 ( 7 + 5 )}{( 7 - 5 ) ( 7 + 5 )}

Expand

2 (7 + 5) : 14 + 25

Expand

(7 - 5) (7 + 5) : 44

= \frac{14 + 2 5}{44}

Factor out common term

2 : 2 (7 + 5)

= \frac{2 ( 7 + 5 )}{44}

Factor the number:

44 = 2 \cdot 22

= \frac{2 ( 7 + 5 )}{2 \cdot 22}

Cancel the common factor:

2

= \frac{7 + 5}{22}

x - \frac{5}{9} = \frac{4}{9}

\frac{2}{3 ( 64 ) ^{\frac{2}{3}}}

- 1 2^{2} + 5^{2} = c^{2}

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

3 x - (\frac{2 x}{3}) < (\frac{1}{2}) + (\frac{3 x}{4})