Question

rationalize the denominator of 2/7-4√3​

Answer 1

Given:

$\frac{2}{7 - 4 \sqrt{3} }$

Multiplying and dividing by by 7 + 4√3,

$\frac{2}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} }$

$= \frac{2(7 + 4 \sqrt{3)} }{ {(7)}^{2} - {(4 \sqrt{3}) }^{2} }$

$= \frac{2(7 + 4 \sqrt{3}) }{49 - 48}$

$= 2(7 + 4 \sqrt{3} )$

$= 14 + 8 \sqrt{3}$