Can you simplify 25p/\2 over 9 by square rooting the numerater and the denominator

25p (the "p" is sqaured)
--------------------------------
9

It is a fraction

I will use the symbol sqrt to mean "square root".

Note that sqrt ( 25 p^2 ) = sqrt (25) * sqrt (p^2) = 5 * p = 5p.
That's for the numerator.
For the denominator sqrt (9) = 3.

So sqrt ( 25p^2/9) = (5p)/3

Hope it helps.

No, that's not a linear operation. Say p is 1, then 25*1*1/9 = 2.778.
If you square root both, you get a new number, 5p/3 = 5*1/3 = 1.667.

The reason is that a square root operation is not linear, meaning it is a curve on a graph. You can only do that with things that make a line on a graph, like dividing both by 3. 3 is a line.

no...you can't take the square root of a fraction and have it be equal to the original fraction.

is 16 = 4?
then 16/1 is not equal to 4/1.

25p²/9 all units are squares, so you can write it as the square of the square roots of the components.
So, yes, (a²p²/b²) = (ap/b)²

No. 25P^2/9=5p*5p/(3*3) and this is not equal to 5p/3.