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

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

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

simplify

\frac{3}{5 + 2}

5 - 2

Decimal Notation

0.82185 \dots

Solution steps

\frac{3}{5 + 2}

Multiply by the conjugate

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

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

Expand

3 (5 - 2) : 35 - 32

Expand

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

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

Factor out common term

3

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

Cancel the common factor:

3

= 5 - 2

6 x - 3 x

5 x \cdot 3 x

\frac{\frac{x - 2}{2}}{\frac{x ^{2} - 4}{3}}

\frac{sin ( x )}{1 - cos ( x )} - csc (x)

(1 - 2 m + 5 m^{2}) (8 - 6 m)

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