Question

Simplifying radical expressions:
\[\frac{\sqrt(2) + \sqrt(5)}{\sqrt(2) - \sqrt(5)}\]
Here is my attempt:
\[\frac{\sqrt(2) + \sqrt(5) * \sqrt(2) - \sqrt(5)}{\sqrt(2) - \sqrt(5) * \sqrt(2) - \sqrt(5)}\]
(Multiplying via the conjugate.)
I am not sure where to go from there, the question asks me to simplify to the simplest form.
Any help is appreciate,
Thanks.

Answer 1

you need to multiply by the conjugate of the denominator, not the numerator

Answer 2

\[\frac{\sqrt2 + \sqrt5}{\sqrt2 - \sqrt5}\frac{\sqrt2+\sqrt5}{\sqrt2+\sqrt5}\] is the first step

Answer 3

the denominator is \(2-5=-3\) and the numerator is what you get when you multiply that mess out

Answer 4

\[\dfrac {7 + 2 \sqrt(10)}{-3}\]
My work:
\[{(\sqrt(2) + \sqrt(5))}^2 = \sqrt(2)^2 + 2\sqrt(2)\sqrt(5) + \sqrt(5)^2\]
\[7 + 2 \sqrt(10)\]
\[2 - 5 = -3\]
\[\dfrac{7 + 2 \sqrt(10)}{-3}\]

Thank you,
I understand. Brilliant!

Answer 5

looks good to me