What is 4/(5-sqrt(2)) ?

The solution to 4/(5-sqrt(2)) is (20+4sqrt(2))/(23)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4/(5-sqrt(2))

simplify

\frac{4}{5 - 2}

\frac{20 + 4 2}{23}

Decimal Notation

1.11551 \dots

Solution steps

\frac{4}{5 - 2}

Multiply by the conjugate

\frac{5 + 2}{5 + 2}

= \frac{4 ( 5 + 2 )}{( 5 - 2 ) ( 5 + 2 )}

Expand

4 (5 + 2) : 20 + 42

Expand

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

= \frac{20 + 4 2}{23}

\frac{5 2}{4}

\frac{6 x}{\frac{3 x}{4}}

\frac{x ^{2} - 12 x + 20}{5 x ^{2} + 25 x - 70}

- 5 \cdot - 5

3 \times \frac{3}{2}