Answer:
[tex]\frac{\sqrt{3}}{3}[/tex]
Step-by-step explanation:
So we start with the original expression to be:
[tex]\sqrt{\frac{1}{3}}[/tex]
so we need to first split the square root into two, one for the numerator and another one for the denominator so we get:
[tex]\frac{\sqrt{1}}{\sqrt{3}}[/tex]
we can now simplify that so we get:
[tex]\frac{1}{\sqrt{3}}[/tex]
we can now rationalize the denominator by multiplying the fraction by [tex]\frac{\sqrt{3}}{\sqrt{3}}[/tex]
so we get:
[tex]\frac{1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}[/tex]
we do the multiplication so we end up with:
[tex] \frac{\sqrt{3}}{(\sqrt{3})^{2}} [/tex]
which simplifies to:
[tex]\frac{\sqrt{3}}{3}[/tex]
