Question

Rationalise 2+√3/2-√3
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Answer 1

Answer:

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Answer 2

ANSWER:

To Rationalize:

• (2 + √3)/(2 - √3)

Solution:

We are given that,

$\implies\dfrac{2+\sqrt3}{2-\sqrt3}$

Now, we need to rationalize. So, we see the denominator.

The denominator is 2 - √3, and the rationalising factor of it will be 2 + √3.

So,

$\implies\dfrac{2+\sqrt3}{2-\sqrt3}$

Multiplying and dividing by 2 + √3.

$\implies\dfrac{2+\sqrt3}{2-\sqrt3}\times\dfrac{2+\sqrt3}{2+\sqrt3}$

Combining the fractions,

$\implies\dfrac{(2+\sqrt3)(2+\sqrt3)}{(2-\sqrt3)(2+\sqrt3)}$

We know that,

$\hookrightarrow (a+b)(a-b)=a^2-b^2$

So,

$\implies\dfrac{(2+\sqrt3)^2}{(2-\sqrt3)(2+\sqrt3)}$

$\implies\dfrac{(2+\sqrt3)^2}{(2)^2-(\sqrt3)^2}$

We know that,

$\hookrightarrow (a+b)^2=a^+-b^2+2ab$

So,

$\implies\dfrac{(2+\sqrt3)^2}{(2)^2-(\sqrt3)^2}$

$\implies\dfrac{(2)^2+(\sqrt3)^2+2(2)(\sqrt3)}{4-3}$

$\implies\dfrac{4+3+4\sqrt3}{1}$

$\implies\bf7+4\sqrt3$

Therefore,

$\implies\bf\dfrac{2+\sqrt3}{2-\sqrt3}=7+4\sqrt3$