Question

2√6-√5
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3√5-2√6​

Answer 1

Answer:

$\frac{2\sqrt{6}-\sqrt{5} }{3\sqrt{5}-2\sqrt{6} }=\frac{4\sqrt{30}+9}{21}$

Step-by-step explanation:

$\frac{2\sqrt{6}-\sqrt{5} }{3\sqrt{5}-2\sqrt{6} }$

Rationalize the denominator by multiplying it by $\frac{3\sqrt{5} +2\sqrt{6}}{3\sqrt{5} +2\sqrt{6}}$

$\frac{2\sqrt{6}-\sqrt{5} }{3\sqrt{5}-2\sqrt{6} } *\frac{3\sqrt{5} +2\sqrt{6}}{3\sqrt{5} +2\sqrt{6}}$

by the formula $x^{2} - y^{2} = (x+y)(x-y)$

$\frac{(2\sqrt{6}-\sqrt{5})*(3\sqrt{5} +2\sqrt{6})}{(3\sqrt{5})^{2} -(2\sqrt{6} )^{2} } =$ $\frac{2\sqrt{6}*(3\sqrt{5}+2\sqrt{6}) - \sqrt{5}*(3\sqrt{5}+2\sqrt{6}) }{9*5-4*6}$

$=\frac{6\sqrt{5*6} +4\sqrt{6*6} - 3\sqrt{5*5} - 2\sqrt{5*6} } {21}$ $=\frac{6\sqrt{30}-2\sqrt{30}+6*4-3*5 }{21}$ $=\frac{4\sqrt{30}+9}{21}$

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