Simplify a Radical

Change the factors of 4x² to perfect squares.

4 = 2²
x² is already a perfect square.

So √4x² = √2²⋅x².

Take the squared factors, 2 and x,
out from the square root.

Then √2²⋅x² = 2x.

So 2x is the answer.

Change the factors of 5a²bc⁶ to perfect squares
as much as you can.

a² is already a perfect square.
c⁶ = c^3⋅2 = (c³)²

Power of a Power

Take the squared factors, a and c³,
out from the square root.

And leave the non-squared factors, 5 and b,
in the square root.

So ac³√5b is the answer.

Change the coefficient 12 to its prime factorization:
12 = 2²⋅3.

x⁹ is an odd power.

To make a perfect square,
split x⁹ to x⁸ and x.

x⁸ is an even power,
which will be a perfect square.

Change the factors of 2²⋅3⋅x⁸⋅x to perfect squares
as much as you can.

2² is already a perfect square.
x⁸ = x^4⋅2 = (x⁴)²

Take the squared factors, 2 and x⁴,
out from the square root.

And leave the non-squared factors, 3 and x,
in the square root.

So 2x⁴√3x is the answer.