First the long way, then the shortcut:
 ______
√16x⁸y⁴

16 = 4‧4 = 2‧2‧2‧2
x⁸ = x‧x‧x‧x‧x‧x‧x‧x
y⁴= y‧y‧y‧y

 _________________________
√2‧2‧2‧2‧x‧x‧x‧x‧x‧x‧x‧x‧y‧y‧y‧y

Divide up into as many groups of 2 like factors
as possible:

 _________________________________________
√(2‧2)‧(2‧2)‧(x‧x)‧(x‧x)‧(x‧x)‧(x‧x)‧(y‧y)‧(y‧y)

Write each pair as a square:

 ____________________
√2²‧2²‧x²‧x²‧x²‧x²‧y²‧y²

Take the individual square roots:

 __ __  __  __ __  __ __  __
√2²‧√2²‧√x²‧√x²‧√x²‧√x²‧√y²‧√y²

The square roots and the squares cancel out,
so you erase all the squares and the square roots:

2‧2‧x‧x‧x‧x‧y‧y

4x⁴y²

Here is the one step short-cut:
 ______
√16x⁸y⁴



The square root of 16 is 4.
Take the square root of x⁸ by dividing the 
exponent by 2, to get x⁴

Take the square root of y⁴by dividing the 
exponent by 2, to get y²

Write:

4x⁴y²

Edwin