What is (sqrt(10)-sqrt(5))/(sqrt(5)+\sqrt{2)} ?

The solution to (sqrt(10)-sqrt(5))/(sqrt(5)+\sqrt{2)} is (5sqrt(2)-2sqrt(5)-5+sqrt(10))/3

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simplify (sqrt(10)-sqrt(5))/(sqrt(5)+\sqrt{2)}

simplify

\frac{10 - 5}{5 + 2}

\frac{5 2 - 2 5 - 5 + 10}{3}

Decimal Notation

0.25373 \dots

Solution steps

\frac{10 - 5}{5 + 2}

Multiply by the conjugate

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

= \frac{( 10 - 5 ) ( 5 - 2 )}{( 5 + 2 ) ( 5 - 2 )}

Expand

(10 - 5) (5 - 2) : 52 - 25 - 5 + 10

Expand

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

= \frac{5 2 - 2 5 - 5 + 10}{3}

- 5 (5 z - 6) < - 30 z + 10

8 x^{2} + 16 x = 24

(x + 4) (x^{2} - 5 x - 14) \geq 0

(x - 7)^{2} (x + 8) > 0

- 2 - 3

What is (sqrt(10)-sqrt(5))/(sqrt(5)+\sqrt{2)} ?
The solution to (sqrt(10)-sqrt(5))/(sqrt(5)+\sqrt{2)} is (5sqrt(2)-2sqrt(5)-5+sqrt(10))/3