Question

simplyfy by rationalizing the denominator 6-4root 2 / 6+4root2

Answer 1

$\bf \large \it{Hey \: User!!!}$

$\bf \: given \: = > \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \\ \\ \bf \: = \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} } \\ \\ \bf = \frac{(6 - 4 \sqrt{2})(6 - 4 \sqrt{2}) }{(6 + 4 \sqrt{2} )(6 - 4 \sqrt{2} )} \\ \\ \bf = \frac{ {(6 - 4 \sqrt{2}) }^{2} }{ {(6)}^{2} - {(4 \sqrt{2} })^{2} } \\ \\ \bf \: = \frac{ {6}^{2} - 2(6)(4 \sqrt{2}) + {(4 \sqrt{2} )}^{2} }{36 - 32} \\ \\ \bf = \frac{36 - 48 \sqrt{2} + 32 }{4} \\ \\ \bf = \frac{68 - 48 \sqrt{2} }{4} \\ \\ \bf = 17 - 12 \sqrt{2}$

$\bf \large \it{Cheers!!!}$