Doubt from Greg's Quant Tips & Tricks Session 4

[rehanluthra88]

Hey Everyone,

I was watching Greg’s “Tips, Tricks & Shortcuts” video 4 and came across the following problem:

In the video, Greg says n^2 must be divisible by 2^3 * 3^2 (prime factorization of 72), which I totally understand. However, he then goes onto say “square rooting the whole thing to give us n would mean that we need one 3 and two 2’s”. I understand how square rooting 3^2 would mean one three, but square rooting 2^3 means 2^3/2. So how does he determine that we need “two 2’s” and not just “one 2”?

Similarly, in another questions that’s almost identical to the one above

He follows the same procedure and take the square root of the entire expression to conclude that m must have two 2’s (which I understand since square root of 2^4 is 2^2), but “one 3”. How? The square root of 3^1 is not 3^1? Can it not also mean that we need 0 three’s?

If anyone could help clarify, it would be much appreciated!

Thank you so much

[Leaderboard]

Look from the perspective of n. n must have at least 2 2s and 1 3. Squaring it would get you something of the form 2^4 3^2.

You cannot reduce the number of 2s or 3s as in that case n^2 won’t divide 72.

[rehanluthra88]

Ahhh I see, so basically n must have two 2’s, so that when you square it you get 2^4 (which is enough to cover the 2^3 needed). Got it, thanks!