Question

question
express in simplest form with a rational denominator.
\\(\frac{1}{\sqrt{40}}\\)
answer: (manage: one of in)

Explanation:

Step1: Simplify the square root

First, we simplify $\sqrt{40}$. We can factor 40 as $4\times10$, and since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$), we have $\sqrt{40}=\sqrt{4\times10}=\sqrt{4}\times\sqrt{10}=2\sqrt{10}$. So the original expression $\frac{1}{\sqrt{40}}$ becomes $\frac{1}{2\sqrt{10}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{10}$. This is because when we multiply $\sqrt{10}$ by itself, we get 10, which is a rational number. So we have:

$$ \frac{1}{2\sqrt{10}}\times\frac{\sqrt{10}}{\sqrt{10}}=\frac{\sqrt{10}}{2\times10}=\frac{\sqrt{10}}{20} $$

Answer:

$\frac{\sqrt{10}}{20}$