Question

1/√4-√3= ? please answer... I need this one​

Answer 1

Step-by-step explanation:

the answer is 2+√3

please mark as brainliest

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\sf{ \frac{1}{ \sqrt{4} - \sqrt{3} } }$

$\bf \underline{To find-}$

$\textsf{Rationalising the denominator.}$

$\bf \underline{Solution-}$

$\textsf{Given fraction,}$

$\sf{ \frac{1}{ \sqrt{4} - \sqrt{3} } }$

$\textsf{The denominator is √4 - √3.}$

$\textsf{We know that}$

$\textsf{Rationalising factor of √a - √b = √a + √b.}$

$\textsf{Therefore, the rationalising factor of √4 - √3 = √4 + √3.}$

$\textsf{On rationalising the denominator them}$

$\sf{ \Rightarrow \: \frac{1}{ \sqrt{4} - \sqrt{3} } \times \frac{ \sqrt{4} + \sqrt{3} }{ \sqrt{4} + \sqrt{3} } }$

$\sf{ \Rightarrow \: \frac{1( \sqrt{4} + \sqrt{3} )}{( \sqrt{4} - \sqrt{3})( \sqrt{4} + \sqrt{3}) } }$

$\sf{ \Rightarrow \: \frac{\sqrt{4} + \sqrt{3} }{( \sqrt{4} - \sqrt{3})( \sqrt{4} + \sqrt{3}) } }$

$\textsf{Now, comparing the denominator with (a-b)(a+b), we get}$

$\textsf{ \: \: \: \: \: a = √4 and b = √3.}$

$\textsf{Using identity (a-b)(a+b) = a²-b², we get}$

$\sf{ \Rightarrow \: \frac{ \sqrt{4} + \sqrt{3} }{( \sqrt{4} {)}^{2} - ( \sqrt{3} {)}^{2} } }$

$\sf{ \Rightarrow \: \frac{ \sqrt{4} + \sqrt{3} }{4 - 3} }$

$\sf{ \Rightarrow \: \frac{ \sqrt{4} + \sqrt{3} }{1} }$

$\sf{ \Rightarrow \: \sqrt{4} + \sqrt{3} }$

$\bf \underline{Hence, the\: denominator \: is \: rationalised.}$