Question

rationalize the denominator of 2 + root 3 upon 2 minus root 3

Answer 1

Question

$\sf \large \: \dfrac{2 + \sqrt{3} }{2 - \sqrt{3} }$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Rationalising means removing root values from the denominator and shifting towards the numerator.

Step by step explanation:

1. First we check the root values in the denominator.
2. Second step is to multiply both numerator and denominator with the opposite sign of denominator.
3. Simplify upto certain limit and it's your Required answer.

$\sf \longmapsto \dfrac{2 + \sqrt{3} }{2 - \sqrt{3} }$

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

An identity used here:

(a+b)²=a²+b²+2ab

(a+b)²=a²+b²+2ab(a+b)(a-b)=a²-b²

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

$\sf \longmapsto \dfrac{ {(2)}^{2} + {( \sqrt{3} )}^{2} + 2(2)( \sqrt{3} ) }{4 - 3}$

$\sf \longmapsto4 + 3 + 4 \sqrt{3}$

$\sf = 7 + 4 \sqrt{3}$

Therefore,7+4√3 is your required answer.