Question

simplify.
\\(\frac{\sqrt{5}}{\sqrt{80}}\\)

Explanation:

Step1: Use quotient rule for radicals

The quotient rule for radicals states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ (where $a\geq0$ and $b>0$). So, $\frac{\sqrt{5}}{\sqrt{80}}=\sqrt{\frac{5}{80}}$.

Step2: Simplify the fraction inside the square root

Simplify $\frac{5}{80}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5. So, $\frac{5\div5}{80\div5}=\frac{1}{16}$. Now we have $\sqrt{\frac{1}{16}}$.

Step3: Evaluate the square root

We know that $\sqrt{\frac{1}{16}}=\frac{\sqrt{1}}{\sqrt{16}}$ (by the quotient rule for radicals again). Since $\sqrt{1} = 1$ and $\sqrt{16}=4$, this simplifies to $\frac{1}{4}$.

Answer:

$\frac{1}{4}$