Question

Rationalize the denominator of the expression 2 - √ 3 / √ 6

Answer 1

Step-by-step explanation:

$\to \dfrac{2 - \sqrt{3} }{ \sqrt{6} }$

• Conjugate of √a is √a. So, conjugate of √6 is √6. Multiplying √6 with both numerator and denominator.

$\to \dfrac{2 - \sqrt{3} }{ \sqrt{6} } \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\to \dfrac{ \sqrt{6}( 2 - \sqrt{3} )}{ {(\sqrt{6})}^{2} }$

$\to \dfrac{ 2 \sqrt{6} - \sqrt{18} }{ 6 }$

$\to \dfrac{ 2 \sqrt{6} - 3 \sqrt{2} }{ 6 }$

$\to \dfrac{ \sqrt{6}}{3} - \dfrac{ \sqrt{2} }{ 2 }$

Hence, rationalised!