Question

(sqrt{dfrac{81}{2}})

Explanation:

Step1: Simplify the square root of the fraction

We know that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ (where $a\geq0$ and $b > 0$). So for $\sqrt{\frac{81}{2}}$, we can rewrite it as $\frac{\sqrt{81}}{\sqrt{2}}$.

Step2: Calculate the square root of 81

Since $9\times9 = 81$, $\sqrt{81}=9$. So now we have $\frac{9}{\sqrt{2}}$.

Step3: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$. So $\frac{9\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{9\sqrt{2}}{2}$.

Answer:

$\frac{9\sqrt{2}}{2}$