Question

Rationalise the following​

Answer 1

➤ Answer

• -√6 + √12

➤ To Do

• To rationalize the denominator $\cfrac{3 \sqrt{2} }{\sqrt{3} + \sqrt{6} }$

➤ Step By Step Explanation

Given a number $\cfrac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} }$. We need to rationalize it's denominator.

So let's do it !!

➠ Using Identity

$\dag \underline{\boxed{ \sf{ \purple{(x + y)(x - y) = {x}^{2} - {y}^{2}}}}}$

➠ Solution

$\longmapsto\tt\cfrac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } \\ \\ \longmapsto\tt\cfrac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } \times \cfrac{ \sqrt{3} - \sqrt{6} }{ \sqrt{3} - \sqrt{6} } \\ \\\longmapsto\tt \cfrac{3 \sqrt{2} \times( \sqrt{3} - \sqrt{6})}{({\sqrt{3})}^{2} - {(\sqrt{6})}^{2} } \\ \\ \longmapsto\tt \cfrac{3 \sqrt{2} \times \sqrt{3} - 3 \sqrt{2} \times \sqrt{6}}{3 - 6} \\ \\\longmapsto\tt \cfrac{3 \sqrt{6} - 3 \sqrt{12} }{ - 3} \\ \\\longmapsto\tt \cfrac{ \not3( \sqrt{6} - \sqrt{12})}{ - \not3} \\ \\\longmapsto\tt - (\sqrt{6} - \sqrt{12}) \\ \\\longmapsto\bf{\green{- \sqrt{6} + \sqrt{12}}}$

➵ Hence, rationalized.

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Answer 2

Answer:

I hope it is helpful to you dear mate