Question

rationalize the denominator of the following.
$\frac{2 + \sqrt{3} }{2 - \sqrt{3} }$
​

Answer 1

AnsWer :

7+ 4√3.

Concepts Required :

• Rationalize the denominator, means Multiply nominator and denominator by opposite sign.

Solution :

$\tt= \frac{2 + \sqrt{3} }{2 - \sqrt{3} }$

$\tt= \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

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

$\tt= \frac{4 + 3 + 4 \sqrt{3} } {4 - 3}$

$\tt= \frac{7 + 4 \sqrt{3} } {1}$

$\tt= {7 + 4 \sqrt{3} }.$

$\rule{200}3$

Formula Use :

• (a + b)² = a² + b² + 2ab.
• (a + b )(a - b) = a² - b².