Question

question 15 of 25
simplify the radical expression below.
\\(\sqrt{\frac{2}{9}}\\)
\\(\bigcirc\\) a. \\(\frac{2}{9}\\)
\\(\bigcirc\\) b. \\(\frac{\sqrt{2}}{9}\\)
\\(\bigcirc\\) c. \\(\frac{2}{3}\\)
\\(\bigcirc\\) d. \\(\frac{\sqrt{2}}{3}\\)

Explanation:

Step1: Apply radical quotient rule

The quotient rule for radicals states that \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (where \(a\geq0\) and \(b > 0\)). So, for \(\sqrt{\frac{2}{9}}\), we can rewrite it as \(\frac{\sqrt{2}}{\sqrt{9}}\).

Step2: Simplify the denominator

We know that \(\sqrt{9} = 3\) because \(3\times3=9\). Substituting this into the expression from Step 1, we get \(\frac{\sqrt{2}}{3}\).

Answer:

D. \(\frac{\sqrt{2}}{3}\)