Answer: Yes
Step-by-step explanation:
Since the numerator is multiplying square root 13 by square root 2, we can break them apart.
[tex]\displaystyle \frac{\sqrt{13*2}}{\sqrt{13}} =\frac{\sqrt{13}*\sqrt{2} }{\sqrt{13}}[/tex]
You are correct, [tex]\sqrt{13}[/tex] over [tex]\sqrt{13}[/tex] is equal to one, so we can "cancel them out" of our expression.
[tex]\displaystyle \frac{\sqrt{13} }{\sqrt{13}} = 1[/tex]
This leaves us with: [tex]\sqrt{2}[/tex]
We can also test this by using a calculator:
[tex]\frac{\sqrt{13*2}}{\sqrt{13}} \approx 1.41421356\\\sqrt{2} \approx 1.41421356\\1.41421356=1.41421356[/tex]
