Math, asked by alempreeti25, 3 months ago

rationalise the denominator of 1 /2+root 3​

Answers

Answered by Anonymous
12

\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

______________________

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}

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