Question

12. Simplify:- 6/2√3-√6 + √6/√3+√2 - 4√3/√6-√2


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Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

We have to simplify the given expression. Lets start!

$\tt=\dfrac{6}{2\sqrt{3}-\sqrt{6}}+\dfrac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\dfrac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}$

$\tt=\dfrac{6\times(2\sqrt{3}+\sqrt{6})}{(2\sqrt{3}-\sqrt{6})(2\sqrt{3}+\sqrt{6})}+\dfrac{\sqrt{6}\times(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}-\dfrac{4\sqrt{3}\times(\sqrt{6}+\sqrt{2})}{(\sqrt{6}-\sqrt{2})(\sqrt{6}+\sqrt{2})}$

Using identity (a + b)(a - b) = a² - b², simplify the given expression,

$\tt=\dfrac{6\times(2\sqrt{3}+\sqrt{6})}{12-6}+\dfrac{\sqrt{6}\times(\sqrt{3}-\sqrt{2})}{3-2}-\dfrac{4\sqrt{3}\times(\sqrt{6}+\sqrt{2})}{6-2}$

$\tt=\dfrac{6\times(2\sqrt{3}+\sqrt{6})}{6}+\sqrt{6}\times(\sqrt{3}-\sqrt{2})-\dfrac{4\sqrt{3}\times(\sqrt{6}+\sqrt{2})}{4}$

$\tt=2\sqrt{3}+\sqrt{6}+\sqrt{6}\times(\sqrt{3}-\sqrt{2})-\sqrt{3}\times(\sqrt{6}+\sqrt{2})$

$\tt=2\sqrt{3}+\sqrt{6}+\sqrt{18}-\sqrt{12}-\sqrt{18}-\sqrt{6}$

$\tt=2\sqrt{3}-\sqrt{12}$

$\tt=2\sqrt{3}-\sqrt{4\times3}$

$\tt=2\sqrt{3}-2\sqrt{3}$

$\tt=0$

⊕ So, the answer is 0.

$\texttt{\textsf{\large{\underline{Concept}:}}}$

• Rationalization: The process of multiplying a surd by another surd to get a rational number is called rationalization. Using rationalization, we have omitted all the surds from the denominator part of the fraction. In this way, the problem is solved.