How do you write this expression with a rationalized denominator?

5 * sqrt(3) / 2 - sqrt(3)

Question

How do you write this expression with a rationalized denominator?

5 * sqrt(3) / 2 - sqrt(3)

anonymous · Answer

I get as far as $$\frac{ 5\sqrt{3} }{ 2 - \sqrt{3} } * \frac{ 2 + \sqrt{3} }{ 2 + \sqrt{3} }$$

and then i'm stuck

isaiah.feynman · Answer

Open study won't show the expression properly.

anonymous · Answer

ugh

[5 * sqrt(3) /  2 - sqrt(3)] * [2 + sqrt(3) / 2 + sqrt(3)]

anonymous · Answer

@ganeshie8 help please?

ganeshie8 · Answer

thats a very good start,
next multiply numerator separately
multiply denominator separately

ganeshie8 · Answer

$\large     \frac{ 5\sqrt{3} }{ 2 - \sqrt{3} } * \color{red}{\frac{ 2 + \sqrt{3} }{ 2 + \sqrt{3} }} $


$\large     \frac{ 5\sqrt{3} \color{red}{(2+\sqrt{3})}}{ (2 - \sqrt{3})\color{red}{(2+\sqrt{3})} } $

ganeshie8 · Answer

remember the identity (a+b)(a-b) = a^2 - b^2  ?

anonymous · Answer

yeah.... so

10 sqrt(3) + 15 / 4 - 3

4 -3 = 1 so

15 + 10 sqrt(3)

is that right?

ganeshie8 · Answer

$\huge \color{red}{\checkmark}$

anonymous · Answer

thank you!!

ganeshie8 · Answer

np =)