What is (3sqrt(5)-4)/(sqrt(5)-2) ?

The solution to (3sqrt(5)-4)/(sqrt(5)-2) is 7+2sqrt(5)

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simplify (3sqrt(5)-4)/(sqrt(5)-2)

simplify

\frac{3 5 - 4}{5 - 2}

7 + 25

Decimal Notation

11.47213 \dots

Solution steps

\frac{3 5 - 4}{5 - 2}

Multiply by the conjugate

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

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

Expand

(35 - 4) (5 + 2) : 7 + 25

Expand

(5 - 2) (5 + 2) : 1

= \frac{7 + 2 5}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 7 + 25

\frac{7}{3} + \frac{2}{5} + \frac{1}{3}

(- i) i

2. 2^{3}

(\frac{- 1}{2})^{\frac{- 1}{2}}

14 - \frac{1}{7}

What is (3sqrt(5)-4)/(sqrt(5)-2) ?
The solution to (3sqrt(5)-4)/(sqrt(5)-2) is 7+2sqrt(5)