Question

3) Rationalize the denominator:
$\frac{3}{12 \sqrt{6} \times - 3 \sqrt{2} }$
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Answer 1

Answer:

$\frac{3}{12 \sqrt{6} - 3 \sqrt{2} } =\frac{4\sqrt{6}+\sqrt{2}}{94}$

Step-by-step explanation:

$\frac{3}{12 \sqrt{6} - 3 \sqrt{2} }$

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

$=\frac{1}{(4 \sqrt{6} - \sqrt{2} )}$

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

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

$=\frac{4\sqrt{6}+\sqrt{2}}{96-2}$

$=\frac{4\sqrt{6}+\sqrt{2}}{94}$

Therefore,

$\frac{3}{12 \sqrt{6} - 3 \sqrt{2} } =\frac{4\sqrt{6}+\sqrt{2}}{94}$

•••♪

Answer 2

$\huge\sf{Answer:-}$

= 3/12 √6 - √2

= 3/3 (4 √6 - √2)

= 1/(4 √6 - √2)

= 4 √6 + √2 / (4√6 - √2)(4√6 + √2)

= 4 √6 + √2 / (4√6)² - ( √2)²

= 4 √6 + √2 / 96 - 2

= 4 √6 + √2 / 94

So,

= 3 / 12√ - 3 √2

= 4 √6 + √2 / 94

Therefore [.•.] Proved!