Question

rationalize the radicals below. ensure your final answer is as simplified as possible.
\\(\frac{4\sqrt{4}}{7\sqrt{12}} = \\)

Explanation:

Step1: Simplify square roots

Simplify $\sqrt{4}$ and $\sqrt{12}$. We know that $\sqrt{4} = 2$ and $\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}$. So the expression becomes $\frac{4\times2}{7\times2\sqrt{3}}$.

Step2: Cancel common factors

Cancel the common factor of 2 in the numerator and the denominator. The 2 in the numerator (from $4\times2$) and the 2 in the denominator (from $7\times2\sqrt{3}$) cancel out, leaving $\frac{4}{7\sqrt{3}}$.

Step3: Rationalize the denominator

To rationalize the denominator, multiply the numerator and the denominator by $\sqrt{3}$. So we have $\frac{4\times\sqrt{3}}{7\sqrt{3}\times\sqrt{3}}$. Since $\sqrt{3}\times\sqrt{3}=3$, the denominator becomes $7\times3 = 21$ and the numerator becomes $4\sqrt{3}$. So the simplified expression is $\frac{4\sqrt{3}}{21}$.

Answer:

$\frac{4\sqrt{3}}{21}$