Question

express in simplest form with a rational denominator. \\(\dfrac{6}{\sqrt{3}}\\)

Explanation:

Step1: Rationalize the denominator by multiplying numerator and denominator by $\sqrt{3}$

$\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

Step2: Simplify the numerator and denominator

Numerator: $6 \times \sqrt{3} = 6\sqrt{3}$
Denominator: $\sqrt{3} \times \sqrt{3} = 3$
So we have $\frac{6\sqrt{3}}{3}$

Step3: Simplify the fraction

Divide numerator and denominator by 3: $\frac{6\sqrt{3} \div 3}{3 \div 3} = 2\sqrt{3}$

Answer:

$2\sqrt{3}$