What is 3/(sqrt(2)+\sqrt{5)} ?

The solution to 3/(sqrt(2)+\sqrt{5)} is -sqrt(2)+sqrt(5)

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simplify 3/(sqrt(2)+\sqrt{5)}

simplify

\frac{3}{2 + 5}

- 2 + 5

Decimal Notation

0.82185 \dots

Solution steps

\frac{3}{2 + 5}

Multiply by the conjugate

\frac{2 - 5}{2 - 5}

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

Expand

3 (2 - 5) : 32 - 35

Expand

(2 + 5) (2 - 5) : - 3

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

Factor out common term

3

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

Cancel the common factor:

3

= \frac{2 - 5}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (2 - 5)

- (2 - 5) = - 2 + 5

= - 2 + 5

(3 x^{- 3})^{- 2} x^{- 2}

5 (3 x - 11) - 9 x + 30

2 \cdot \frac{3}{7}

(1)^{2} + (2)^{2}

a^{0} \cdot a^{6}

What is 3/(sqrt(2)+\sqrt{5)} ?
The solution to 3/(sqrt(2)+\sqrt{5)} is -sqrt(2)+sqrt(5)