Question

$(6 - 4 \sqrt{2}) \div (6 + 4 \sqrt{2})$
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Answer 1

Answer:

17 - 12√2

Step-by-step explanation:

$= \frac{(6 - 4 \sqrt{2} )}{(6 + 4 \sqrt{2} )} . \frac{(6 - 4 \sqrt{2}) }{(6 - 4 \sqrt{2} )} \\ = \frac{6(6 - 4 \sqrt{2} ) - 4 \sqrt{2}(6 - 4 \sqrt{2} ) }{6(6 - 4 \sqrt{2} ) + 4 \sqrt{2} (6 - 4 \sqrt{2} )} \\ = \frac{36 - 24 \sqrt{2} - 24 \sqrt{2} + 16 \sqrt{4} }{36 -16 \sqrt{4} } \\ = \frac{36 - 48 \sqrt{2} + 16(2) }{36 - 16(2)} \\ = \frac{68 - 48 \sqrt{2} }{4} \\ = 17 - 12 \sqrt{2} \p$