Here we will show you two methods that you can use to simplify the square root of 32. In other words, we will show you how to find the square root of 32 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√32 = A√B

**Greatest Perfect Square Factor Method**

The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32 to simplify the square root of 32. This is how to calculate A and B using this method:

**A**= Calculate the square root of the greatest perfect square from the list of all factors of 32. The factors of 32 are 1, 2, 4, 8, 16, and 32. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

**B**= Calculate 32 divided by the greatest perfect square from the list of all factors of 32. We determined above that the greatest perfect square from the list of all factors of 32 is 16. Furthermore, 32 divided by 16 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 32 in its simplest radical form as follows:

√32 = A√B

**√32 = 4√2**

**Double Prime Factor Method**

The Double Prime Factor Method uses the prime factors of 32 to simplify the square root of 32 to its simplest form possible. This is how to calculate A and B using this method:

**A**= Multiply all the double prime factors (pairs) of 32 and then take the square root of that product. The prime factors that multiply together to make 32 are 2 x 2 x 2 x 2 x 2. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

**B**= Divide 32 by the number (A) squared. 4 squared is 16 and 32 divided by 16 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 32 in its simplest radical form as follows:

√32 = A√B

**√32 = 4√2**

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