Question

What is the following quotient?

Answer 1

Answer:

$\frac{\sqrt{3} }{4}$

Step-by-step explanation:

$\frac{1}{1+\sqrt{3} }$

basically we want to get rid of the √3 on the denominator

to do so we multiply it by itself so it is a perfect square

but whatever we do to the top we must do to the bottom so we multiply the numerator and denominator by √3

$\frac{1*\sqrt{3} }{1+\sqrt{3}*\sqrt{3} }=\frac{\sqrt{3} }{1+\sqrt{9} } =\frac{\sqrt{3} }{1+3} =\frac{\sqrt{3} }{4}$

notes : √3 × √3 = √9 which is a perfect square that simplfies to 3