Question

express in simplest form with a rational denominator.
\\(\frac{7}{\sqrt{10}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of \(\frac{7}{\sqrt{10}}\), we multiply the numerator and the denominator by \(\sqrt{10}\) because \(\sqrt{a}\times\sqrt{a}=a\) (for \(a\geq0\)), which will make the denominator a rational number.
So we have \(\frac{7\times\sqrt{10}}{\sqrt{10}\times\sqrt{10}}\).

Step2: Simplify the denominator

Simplify the denominator \(\sqrt{10}\times\sqrt{10}\). Using the property \(\sqrt{a}\times\sqrt{a}=a\) (where \(a = 10\) here), we get \(\sqrt{10}\times\sqrt{10}=10\).
The numerator is \(7\times\sqrt{10}=7\sqrt{10}\).

So the expression becomes \(\frac{7\sqrt{10}}{10}\).

Answer:

\(\frac{7\sqrt{10}}{10}\)