Question

rationalise the denominator of 1 /2+root 3​

Answer 1

$\sf{Answer}$

Step by step explanation :-

Given to rationalise the denominator

$\sf\dfrac{1}{2 + \sf\sqrt{3}}$

Lets do !

Conecpt to know:-

For Rationalising denominator We have to multiply and divide with its Rationalizing factor

Rationalizing factor is nothing but just we have to sign

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So, Rationalizing factor of 2 +$\sf\sqrt{3}$ is 2 - $\sf\sqrt{3}$

So, Multiply and divide with is 2 - $\sf\sqrt{3}$

$\sf\dfrac{1}{2 + \sqrt{3} } \times \sf\dfrac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\sf\dfrac{1 \times 2 - \sqrt{3} }{(2 + \sqrt{3)(2 - \sqrt{3)} } }$

In denomiantor It is in form of ( a + b ) ( a - b) = a² - b²

So, apply the formula

$\sf\dfrac{2 - \sqrt{3} }{(2) {}^{2} - \sqrt({3)} {}^{2} }$

$\sf\dfrac{2 - \sqrt{3} }{4 - 3}$

$\sf\dfrac{2 - \sqrt{3} }{1}$

Hence denomiantor rationalised !

So, after Rationalising of $\sf\dfrac{1}{2 + \sf\sqrt{3}}$ is $\sf\dfrac{2 - \sqrt{3} }{1}$