Question

Rationalize the denominator and simplify: 3sqrt(2)-2sqrt(3)/3sqrt(2)+2sqrt(3)

Answer 1

SOLUTION

TO DETERMINE

Rationalize

$\displaystyle \sf{ \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } }$

EVALUATION

$\displaystyle \sf{ \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } }$

$\displaystyle \sf{ = \frac{{(3 \sqrt{2} - 2 \sqrt{3} )}^{2} }{(3 \sqrt{2} + 2 \sqrt{3} )(3 \sqrt{2} - 2 \sqrt{3})} }$

$\displaystyle \sf{ = \frac{{(3 \sqrt{2} - 2 \sqrt{3} )}^{2} }{{(3 \sqrt{2})}^{2} - {(2 \sqrt{3})}^{2} } }$

$\displaystyle \sf{ = \frac{{(3 \sqrt{2} - 2 \sqrt{3} )}^{2} }{18 - 12 } }$

$\displaystyle \sf{ = \frac{18 + 12 - 12 \sqrt{6} }{18 - 12 } }$

$\displaystyle \sf{ = \frac{30 - 12 \sqrt{6} }{6 } }$

$= 5 - 2 \sqrt{6}$

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Answer 2

Answer:

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Step-by-step explanation:

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