Question

Rationalize the denominator of the following expression and simplify: 5 + sqrt 3/ 2 - sqrt 3

Answer 1

`(5+√(3))/(2-√(3))`

multiply by the conjugate of the denominator

`(5+√(3))/(2-√(3))*(2+√(3))/(2+√(3))`

using the rule:

`(a+b)(a-b)=a^2-b^2`

then,

`(5+√(3))/(2-√(3))*(2+√(3))/(2+√(3))=((5+√(3))(2+√(3)))/(2^2-(√(3))^2)`

simplify

`\begin{gathered} (10+5√(3)+2√(3)+(√(3))^2)/(4-3) \\ (10+5√(3)+2√(3)+3)/(1) \\ 13+7√(3) \end{gathered}`

Answer:

After rationalizing the denominator the simplified expression is:

`13+7√(3)`