Question

How do I simplify the radical expression 6+square root 3 over 5-square root 3?

Answer 1

\[\frac{6+\sqrt3}{5-\sqrt3}\]?

Answer 2

yes

Answer 3

ok i think "simplify" in this case actually means "rationalize the denominator" because there is no such mathematical operation as "simplify"
multiply top and bottom by the conjugate of the denominator
the conjugate of \(5-\sqrt3\) is \(5+\sqrt3\) and this works because
\[(5-\sqrt3)(5+\sqrt3)=5^2-3=22\]

Answer 4

you get
\[\frac{6+\sqrt3}{5-\sqrt3}\times \frac{5+\sqrt3}{5-\sqrt3}\]\[=\frac{(6+\sqrt3)(5+\sqrt3)}{22}\]

Answer 5

then you have to multiply out in the numerator

Answer 6

you got if from here?

Answer 7

I think so. the answer that I got is \[\frac{ 1\sqrt{3} }{ 2 }\]