Question

2+√3 + 1 divided by 2+√3​

Answer 1

2 + √3 + 1 / 2 + √3

Take it as 2 + √3 / 2 + √3 + 1/ 2 +√3

= 1 + 1/2 + √3

rationalise denomatinator

1 + 2 - √3 / 4 - 3

= 3 -√3

or √3 (√3 -1) is the answer.

Answer 2

$\bigstar$ Question:

Find the value of :

• $\frac{(2 + \sqrt{3} + 1) }{(2 + \sqrt{3}) }$

$\bigstar$Given:

• $\frac{(2 + \sqrt{3} + 1) }{(2 + \sqrt{3}) }$

$\bigstar$To find:

The value of :

$\frac{(2 + \sqrt{3} + 1) }{(2 + \sqrt{3}) }$

$\bigstar$ Solution:

$\frac{(2 + \sqrt{3} + 1) }{(2 + \sqrt{3}) } \\ = \frac{(3 + \sqrt{3}) }{(2 + \sqrt{3}) }$

$= \frac{(3)(2) + 3( - \sqrt{3} ) + 2( \sqrt{3} ) + \sqrt{3} \times ( - \sqrt{3}) }{ ({2})^{2} - ({ \sqrt{3}) }^{2} }$

Now, we have to Rationalise the denominator to get a rational number as the denominator.

$= \frac{(3 + \sqrt{3} )(2 - \sqrt{3} )}{(2 + \sqrt{3})(2 - \sqrt{3} ) }$

( By using a² - b² = ( a + b ) ( a - b ))

$= \frac{6 - 3\sqrt{3} + 2 \sqrt{3} - 3}{4 - 3}$

$= \frac{6 - \sqrt{3} - 3 }{1}$

$= 3 - \sqrt{3}$

$\bigstar$Answer:

• Therefore, the answer is 3 - √3