Question

7+ 4 root 3 + 1 divided by 7+4 root 3​

Answer 1

7 + 4√3 + 1/7 + 4√3

First, we rationalize the denominator

=  $\frac{7 + 4\sqrt{3}+1 }{7+4\sqrt{3} }$   *   $\frac{7-4\sqrt{3} }{7-4\sqrt{3} }$

=  $\frac{49-28\sqrt{3}+28\sqrt{3}-48+7-4\sqrt{3} }{49-48}$

=  $\frac{49-48+7-4\sqrt{3} }{1}$

=  1 + 7 - 4√3  

=  8 - 4√3

∴ 7 + 4√3 + 1/7 + 4√3 = 8 - 4√3

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