Simplify a Radical

How to simplify a radical: 3 examples and their solutions.

Example 1

Example

Solution

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.

Example 2

Example

Solution

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

a2 is already a perfect square.
c6 = c3⋅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 ac35b is the answer.

Example 3

Example

Solution

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 = x4⋅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 2x43x is the answer.