Question

2√6-5/3√5-2√6 rationalise​

Answer 1

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Answer 2

$\mathfrak{Question:}$

$\textsf{Rationalise\;the\;following:}$

$\tt{\dfrac{2\sqrt{6}-5 }{3\sqrt{5}-2\sqrt{6} }.}$

$\mathfrak{Solution:}$

$\tt{=\dfrac{2\sqrt{6}-5 }{3\sqrt{5}-2\sqrt{6} }}\\\\\\\tt{=\dfrac{2\sqrt{6}-5 }{3\sqrt{5}-2\sqrt{6} }\times\dfrac{3\sqrt{5}+2\sqrt{6} }{3\sqrt{5} +2\sqrt{6} }}\\\\\\\boxed{\tt{a^2-b^2=(a+b)(a-b)}}\\\\\\\tt{=\dfrac{(2\sqrt{6}-5)(3\sqrt{5}+2\sqrt{6} )}{(3\sqrt{5} )^2-(2\sqrt{6} )^2}}\\\\\\\tt{=\dfrac{6\sqrt{30} +24-15\sqrt{5} -10\sqrt{6} }{45-24}}\\\\\\\tt{=\dfrac{6\sqrt{30} +24-15\sqrt{5} -10\sqrt{6} }{21}}.$