Simplify fully ((4+2root3)(4-2root3))/(root11) \\ You must show all your working

Question

Simplify fully
`((4+2root3)(4-2root3))/(root11) \\`

You must show all your working

Answer 1

Solution:-

`\begin{gathered}\\\implies\quad \sf ((4+2√(3))(4-2√(3)))/(√(11))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf ((4^2-(2√(3))^2))/(√(11))\quad((a+b)(a-b)=a^2-b^2)\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf ((4^2-(2√(3))^2))/(√(11))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (16-(2^2*(√(3))^2))/(√(11))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (16-(4*3))/(√(11))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf ((16-12))/(√(11))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (4)/(√(11))\\\end{gathered}`

Rationalising the denominator -

`\begin{gathered}\\\implies\quad \sf (4(√(11)))/(√(11)(√(11)))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (4(√(11)))/(11)\\\end{gathered}`

Required Answer :-

`\quad\green{ \underline { \boxed{ \sf{ \sf (4√(11))/(11)}}}}`