Question

6 minus 4 root 2 divided by 6 + 4 root 2

Answer 1

Answer:

Given,

$\mathtt{ \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } }$

Now, rationalizing the denominator We get,

$\space$

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

$\space$

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

$\space$

$\: \: \: \: \: = \mathtt{ \frac{36 + 32 - 48 \sqrt{2} }{36 - 32} }$

$\space$

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

$\space$

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

$\space$

$= \bf{\mathtt{ 17 - 12 \sqrt{2} }}$