Question

simplify. \sqrt{\frac{50}{245}}

Explanation:

Step1: Simplify the fraction inside the square root

First, we simplify the fraction $\frac{50}{245}$. We can divide both the numerator and the denominator by their greatest common divisor, which is 5. So, $\frac{50\div5}{245\div5}=\frac{10}{49}$. Now our expression becomes $\sqrt{\frac{10}{49}}$.

Step2: Use the property of square roots

Recall that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ for non - negative $a$ and positive $b$. So, $\sqrt{\frac{10}{49}}=\frac{\sqrt{10}}{\sqrt{49}}$.

Step3: Simplify the square root of the perfect square

We know that $\sqrt{49} = 7$ since $7\times7 = 49$. So, $\frac{\sqrt{10}}{\sqrt{49}}=\frac{\sqrt{10}}{7}$.

Answer:

$\frac{\sqrt{10}}{7}$