Question

rationalize the denominator = 6-4√3/6+4√3​

Answer 1

Answer:

$4 \sqrt{3} - 7$

Step-by-step explanation:

$\dfrac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} }$

$=\left(\dfrac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} }\right) \left(\dfrac{6 - 4 \sqrt{3} }{6 - 4 \sqrt{3} } \right)$

$=\dfrac{(6 - 4 \sqrt{3})^{2} }{6^{2} - (4 \sqrt{3})^{2} }$

$= \dfrac{ {6}^{2} + {(4 \sqrt{3} )}^{2} - 2(6)(4 \sqrt{3} ) }{36 - 48}$

$= \dfrac{36 + 48 - 48 \sqrt{3} }{36 - 48}$

$= \dfrac{84 - 48 \sqrt{3} }{ - 12} = 4 \sqrt{3} - 7$