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

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

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

simplify

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

2 + 10

Decimal Notation

5.16227 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

3 (2 + 5) : 32 + 35

Expand

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

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

Factor out common term

3

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

Cancel the common factor:

- 3

= (2 + 5) 2

(2 + 5) 2 = 2 + 10

= 2 + 10

- 10 < - 5 k - 15 < 25

\frac{3}{2}

3 m^{2} + 7 = 301

5 x y - 2 x^{2} y + 2 x y

n - 7 \leq - 2

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