Population vs SD question (moreso regarding algebra)

[user632]

I understand how to solve this problem, I’m just having a bit of trouble with the basic algebra. To put the ratio in the format of the answer choices, I multiplied by the reciprocal of the denominator. However, since the denominator contains a square root, I canceled out the square root present in the numerator. Can someone explain why this is wrong?

Thank you!

[cylverixxx]

Can you show your work either on paper or with mathjax /latex?

[user632]

Sorry about the delay! Thank you for the help!

[cylverixxx]

That gives you the required answer.

[user632]

But wouldn’t the square roots cancel out? The correct answer contains the square roots.

[cylverixxx]

\sqrt{2} \cdot \sqrt{3} = \sqrt{6}, for example. The square roots didn’t cancel here though, right?

[user632]

Right, that makes sense. Thank you!