Question

simplify.
\sqrt{\frac{32}{18}}
be sure to write your answer in simplest form.

Explanation:

Step1: Simplify the fraction inside the square root

First, we simplify the fraction \(\frac{32}{18}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(\frac{32\div2}{18\div2}=\frac{16}{9}\). Now our expression becomes \(\sqrt{\frac{16}{9}}\).

Step2: Use the property of square roots

Recall the property \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (for \(a\geq0\) and \(b > 0\)). Applying this property to \(\sqrt{\frac{16}{9}}\), we get \(\frac{\sqrt{16}}{\sqrt{9}}\).

Step3: Evaluate the square roots

We know that \(\sqrt{16} = 4\) and \(\sqrt{9}=3\). So, \(\frac{\sqrt{16}}{\sqrt{9}}=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\)