Question

Is it mathematically correct to say that:

Answer 1

Answer: Yes

Step-by-step explanation:

    Since the numerator is multiplying square root 13 by square root 2, we can break them apart.

$\displaystyle \frac{\sqrt{13*2}}{\sqrt{13}} =\frac{\sqrt{13}*\sqrt{2} }{\sqrt{13}}$

   You are correct, $\sqrt{13}$ over  $\sqrt{13}$ is equal to one, so we can "cancel them out" of our expression.

$\displaystyle \frac{\sqrt{13} }{\sqrt{13}} = 1$

   This leaves us with: $\sqrt{2}$

We can also test this by using a calculator:

$\frac{\sqrt{13*2}}{\sqrt{13}} \approx 1.41421356\\\sqrt{2} \approx 1.41421356\\1.41421356=1.41421356$