Question

simplify.
\\(\frac{\sqrt{57}}{\sqrt{3}}\\)

Explanation:

Step1: Use the quotient rule for square roots

The quotient rule for square roots states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ (where $a\geq0$ and $b>0$). Applying this rule to $\frac{\sqrt{57}}{\sqrt{3}}$, we get $\sqrt{\frac{57}{3}}$.

Step2: Simplify the fraction inside the square root

Simplify $\frac{57}{3}$. Since $57\div3 = 19$, the expression becomes $\sqrt{19}$.

Answer:

$\sqrt{19}$