Question

rationalize the radicals below. ensure your final answer is as simplified as possible as possible:
\\( \frac{4\sqrt{25}}{\sqrt{10}} = \\) \boxed{}

Explanation:

Step1: Simplify the square root

First, simplify $\sqrt{25}$. We know that $\sqrt{25} = 5$ because $5\times5 = 25$. So the expression becomes $\frac{4\times5}{\sqrt{10}}=\frac{20}{\sqrt{10}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{10}$. So we have $\frac{20\times\sqrt{10}}{\sqrt{10}\times\sqrt{10}}$. Since $\sqrt{10}\times\sqrt{10}=10$, the expression simplifies to $\frac{20\sqrt{10}}{10}$.

Step3: Simplify the fraction

Now, simplify the fraction $\frac{20\sqrt{10}}{10}$. Dividing 20 by 10 gives 2, so the simplified form is $2\sqrt{10}$.

Answer:

$2\sqrt{10}$