Question

express in simplest form with a rational denominator.\\(\dfrac{5}{\sqrt{7}}\\)

Explanation:

Step1: Identify the radical in the denominator

The fraction is $\frac{5}{\sqrt{7}}$, and the radical in the denominator is $\sqrt{7}$. To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{7}$.

Step2: Multiply numerator and denominator by $\sqrt{7}$

\[
\frac{5}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{5\times\sqrt{7}}{\sqrt{7}\times\sqrt{7}}
\]

Step3: Simplify the denominator

Since $\sqrt{7}\times\sqrt{7} = 7$ (by the property $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$), the fraction becomes $\frac{5\sqrt{7}}{7}$.

Answer:

$\frac{5\sqrt{7}}{7}$