Question 142132
{{{30/(4+sqrt(10))}}}
To simplify this we need something called the conjugate. Basically, all that is is taking the sign from the denominator (+ in this case) and switching it (to - in this case). This makes it so that the denominator will not have a radical. We then multiply the original problem by the modified denominator divided by itself.

={{{30/(4+sqrt(10))=30/(4+sqrt(10))*(4-sqrt(10))/(4-sqrt(10))}}}
Notice that this is not changing the number. We are simply multiplying by 1!

Now multiply it through:
={{{30(4-sqrt(10))/(16-10)=(120-30sqrt(10))/6=20-5sqrt(10)}}}

All I did was use FOIL on the denominator and then simplify (numerator and denominator had a 6 in common). That would be your final answer.