Is it mathematically correct to say that: (√(13*2) )/(√(13) ) so just cancel out the 13's with each other and the answer is going to be √(2)?

Question

Is it mathematically correct to say that:


`(√(13*2) )/(√(13) )`


so just cancel out the 13's with each other and the answer is going to be
`√(2)`?

Answer 1

Answer: Yes

Explanation:

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

`\displaystyle (√(13*2))/(√(13)) =(√(13)*√(2) )/(√(13))`

You are correct,
`√(13)` over
`√(13)` is equal to one, so we can "cancel them out" of our expression.

`\displaystyle (√(13) )/(√(13)) = 1`

This leaves us with:
`√(2)`

We can also test this by using a calculator:

`(√(13*2))/(√(13)) \approx 1.41421356\\√(2) \approx 1.41421356\\1.41421356=1.41421356`