Answer:
[tex]\sqrt{\frac{1}{3} }[/tex]
or
[tex]\frac{\sqrt{3} }{3}[/tex]
Step-by-step explanation:
The expression [tex]\frac{\sqrt{5} }{\sqrt{15} }[/tex] can be simplified by first writing the fraction under one single radical instead of two.
[tex]\frac{\sqrt{5} }{\sqrt{15} } = \sqrt{\frac{5}{15} }[/tex]
5/15 simplifies because both share the same factor 5.
It becomes [tex]\sqrt{\frac{5}{15} } = \sqrt{\frac{1}{3} }[/tex]
This can simplify further by breaking apart the radical.
[tex]\sqrt{\frac{1}{3} } = \frac{\sqrt{1} }{\sqrt{3} } = \frac{1}{\sqrt{3} }[/tex]
A radical cannot be left in the denominator, so rationalize it by multiplying by √3 to numerator and denominator.
[tex]\frac{1}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} } =\frac{\sqrt{3} }{3}[/tex]
