Question

Rationalise the : 2/(√7-√6)​

Answer 1

Answer:

2/(√7-√6)

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Answer 2

The Whole concept rationalizing the fraction is that to make the denominator in the form ( a - b ) × ( a + b ) = a² - b²

Q.   $\frac{2}{\sqrt{7}-\sqrt{6} }$

multiplying and dividing number by  $\frac{\sqrt{7}+\sqrt{6} }{\sqrt{7}+\sqrt{6} }$

⇒    $\frac{2}{\sqrt{7}-\sqrt{6} }$   ×  $\frac{\sqrt{7}+\sqrt{6} }{\sqrt{7}+\sqrt{6} }$

⇒    $\frac{2(\sqrt{7}+\sqrt{6)} }{(\sqrt{7}-\sqrt{6} )(\sqrt{7}+\sqrt{6} )}$

⇒    $\frac{2\sqrt{7}+\sqrt{6} }{(\sqrt{7} )^{2} -(\sqrt{\sqrt{6} } )^{2} }$                                             ∴ ( a - b ) ( a + b ) = a² - b²

⇒     $\frac{2\sqrt{7}+\sqrt{6} }{7-6 }$  

⇒     $2\sqrt{7} +\sqrt{6}$

                     ∴  2√7 + √6 is the rationalized form

Hence Rationalized the number

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