Question

simplify.
\\(\frac{\sqrt{6}}{\sqrt{54}}\\)

Explanation:

Step1: Simplify the fraction inside the square root

Using the property of square roots \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\), we have \(\frac{\sqrt{6}}{\sqrt{54}}=\sqrt{\frac{6}{54}}\).

Step2: Reduce the fraction

Simplify \(\frac{6}{54}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6. So \(\frac{6\div6}{54\div6}=\frac{1}{9}\).

Step3: Take the square root

Now we have \(\sqrt{\frac{1}{9}}\), and since \(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}\) and \(\sqrt{1} = 1\), \(\sqrt{9}=3\), we get \(\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)