Question

Simplify 6-4root2/6+4root2

Answer 1

Answer:

17-12√2

Step-by-step explanation:

Answer 2

Answer:

$1. \: \: \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} }$

$= \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} }$

$= \frac{(6 - 4 \sqrt{2})(6 - 4 \sqrt{2} ) }{(6 + 4 \sqrt{2})(6 - 4 \sqrt{2}) }$

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

$= \frac{ {6}^{2} + {4 \sqrt{2}}^{2} - 2 \times 6 \times 4 \sqrt{2} }{36 - 32}$

$= \frac{36 + 32 - 12 \times 4 \sqrt{2} }{4}$

$= \frac{68 - 48 \sqrt{2} }{4}$

$= \frac{4(17 - 12 \sqrt{2} )}{4}$

$= 17 - 12 \sqrt{2}$

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