Question

express in simplest form with a rational denominator.
\\(\frac{4}{\sqrt{10}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of \(\frac{4}{\sqrt{10}}\), we multiply the numerator and the denominator by \(\sqrt{10}\) (since \(\sqrt{a}\times\sqrt{a}=a\) for non - negative \(a\)).
So we have \(\frac{4\times\sqrt{10}}{\sqrt{10}\times\sqrt{10}}\)

Step2: Simplify the expression

First, simplify the denominator: \(\sqrt{10}\times\sqrt{10} = 10\) (by the property \(\sqrt{a}\times\sqrt{a}=a\) where \(a = 10\)).
The numerator is \(4\times\sqrt{10}=4\sqrt{10}\).
So the expression becomes \(\frac{4\sqrt{10}}{10}\).
Then we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\(\frac{4\sqrt{10}\div2}{10\div2}=\frac{2\sqrt{10}}{5}\)

Answer:

\(\frac{2\sqrt{10}}{5}\)