Question

simplify
\frac{\sqrt{24}}{\sqrt{34}}

hint- always look for the most simplified form :)

\bigcirc \frac{\sqrt{816}}{34}

\bigcirc \frac{\sqrt{204}}{17}

\bigcirc \frac{17\sqrt{51}}{2}

\bigcirc \frac{2\sqrt{51}}{17}

Explanation:

Step1: Use the quotient rule of square roots

The quotient rule states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So, $\frac{\sqrt{24}}{\sqrt{34}}=\sqrt{\frac{24}{34}}$.

Step2: Simplify the fraction inside the square root

Simplify $\frac{24}{34}$ by dividing numerator and denominator by 2: $\frac{24\div2}{34\div2}=\frac{12}{17}$. Now we have $\sqrt{\frac{12}{17}}$.

Step3: Rationalize the denominator

To rationalize the denominator, multiply numerator and denominator inside the square root by 17: $\sqrt{\frac{12\times17}{17\times17}}=\frac{\sqrt{204}}{17}$. But we can simplify $\sqrt{204}$ further. Factor 204: $204 = 4\times51$, so $\sqrt{204}=\sqrt{4\times51}=2\sqrt{51}$. Substituting back, we get $\frac{2\sqrt{51}}{17}$.

Answer:

$\frac{2\sqrt{51}}{17}$ (the last option: $\boldsymbol{\frac{2\sqrt{51}}{17}}$)