Question

Rationalize the denominator of the expression. Then simplify 4/(7-sqrt{3})

Answer 1

multiply by the conjugate

Answer 2

\[\frac{4}{7-\sqrt{3}}\]
\[=\frac{4}{7-\sqrt{3}}\times \frac{7+\sqrt{3}}{7+\sqrt{3}}\] is a start

Answer 3

and the reason this works, is that \((a-b)(a+b)=a^2-b^2\) and so \((7-\sqrt{3})(7+\sqrt{3})=7^2-\sqrt{3}^2=49-3=46\)

Answer 4

therefore you denominator is a whole number, namelyl \(46\) and your numerator is \(4(7+\sqrt{3})\) giving you a "final answer" of
\[\frac{4(7+\sqrt{3})}{46}\]

Answer 5

Well after i worked it out, you missed a step in simplificatoin at the end, where the final product would be \[14+2\sqrt{3}/23\]