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

The solution to (2sqrt(5)-sqrt(2))/(sqrt(5)+\sqrt{2)} is 4-sqrt(10)

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

simplify

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

4 - 10

Decimal Notation

0.83772 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(25 - 2) (5 - 2) : 12 - 310

Expand

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

= \frac{12 - 3 10}{3}

Factor out common term

3 : 3 (4 - 10)

= \frac{3 ( 4 - 10 )}{3}

Cancel the common factor:

3

= 4 - 10

\frac{4}{3} \cdot 9

(3 k^{4})^{4}

3 x^{2} - 9 = 7 x

3 x - 2 + 2 x + 5 = 3 (x + 5)

x^{2} - 7 x + 6 = 0

What is (2sqrt(5)-sqrt(2))/(sqrt(5)+\sqrt{2)} ?
The solution to (2sqrt(5)-sqrt(2))/(sqrt(5)+\sqrt{2)} is 4-sqrt(10)