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

The solution to (3+sqrt(5))/(3-sqrt(5)) is (7+3sqrt(5))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (3+sqrt(5))/(3-sqrt(5))

simplify

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

\frac{7 + 3 5}{2}

Decimal Notation

6.85410 \dots

Solution steps

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

Multiply by the conjugate

\frac{3 + 5}{3 + 5}

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

Expand

(3 + 5) (3 + 5) : 14 + 65

Expand

(3 - 5) (3 + 5) : 4

= \frac{14 + 6 5}{4}

Factor out common term

2 : 2 (7 + 35)

= \frac{2 ( 7 + 3 5 )}{4}

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 7 + 3 5 )}{2 \cdot 2}

Cancel the common factor:

2

= \frac{7 + 3 5}{2}

0. 6^{4}

4 m - 4 - 8 = - 2 m + 12

\frac{7}{12} + \frac{5}{8}

4 (x + 3) - (1 - x) = 1

∣ x - 5 ∣ = - 10

What is (3+sqrt(5))/(3-sqrt(5)) ?
The solution to (3+sqrt(5))/(3-sqrt(5)) is (7+3sqrt(5))/2