The author starts by giving the example $\displaystyle 25z^2 - 81y^2$, which equals $\displaystyle (5z + 9y) (5z - 9y)$.

Both 81, and 25 are perfect squares so this makes sense.

$\displaystyle \sqrt{25} = 5*5, \sqrt{9} = 3*3$

Then the author uses this example factoring $\displaystyle x^4 - y^6$

Which equals $\displaystyle (x^2 + y^3)(x^2 - y^3)$.

But this does not make sense to me

$\displaystyle \sqrt{4} = 2 * 2, \sqrt{6} = 2.45...$

Can some one please help clarify what I am doing wrong and how the author is pulling y^3 out of y^6 in the second example?

Many thanks