Question

Help me solve this problem 3 ------ 5+square root 41

Answer 1

Ya want to rationalize the denomenator
if we mutliply the whole thing by (√41)/(√41), we wil still have a √ there messing things up

we need to remember the difference of 2 perfect squares

remember
(a+b)(a-b)=a²-b²

so, we can see the denomenator is 5+√41
multiply the whole fraction by $\frac{5-\sqrt{41}}{5-\sqrt{41}}$

we get
$\frac{3(5-\sqrt{41})}{5^2-(\sqrt{41})^2}=\frac{15-3\sqrt{41}}{25-41}=$
$\frac{15-3\sqrt{41}}{-16}=\frac{-15+3\sqrt{41}}{16}$