Simplify Square Root of 72000

Here we will show you two methods that you can use to simplify the square root of 72000. In other words, we will show you how to find the square root of 72000 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.

√72000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72000 to simplify the square root of 72000. 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 72000. The factors of 72000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000, and 72000. Furthermore, the greatest perfect square on this list is 14400 and the square root of 14400 is 120. Therefore, A equals 120.

B = Calculate 72000 divided by the greatest perfect square from the list of all factors of 72000. We determined above that the greatest perfect square from the list of all factors of 72000 is 14400. Furthermore, 72000 divided by 14400 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 72000 in its simplest radical form as follows:

√72000 = A√B

√72000 = 120√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72000 to simplify the square root of 72000 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 72000 and then take the square root of that product. The prime factors that multiply together to make 72000 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 14400 and the square root of 14400 is 120. Therefore, A equals 120.

B = Divide 72000 by the number (A) squared. 120 squared is 14400 and 72000 divided by 14400 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 72000 in its simplest radical form as follows:

√72000 = A√B

√72000 = 120√5

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 72001
Here is the next square root on our list that we have simplifed for you.