Simplify Square Root of 72600

Here we will show you two methods that you can use to simplify the square root of 72600. In other words, we will show you how to find the square root of 72600 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.

√72600 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72600 to simplify the square root of 72600. 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 72600. The factors of 72600 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 121, 132, 150, 165, 200, 220, 242, 264, 275, 300, 330, 363, 440, 484, 550, 600, 605, 660, 726, 825, 968, 1100, 1210, 1320, 1452, 1650, 1815, 2200, 2420, 2904, 3025, 3300, 3630, 4840, 6050, 6600, 7260, 9075, 12100, 14520, 18150, 24200, 36300, and 72600. Furthermore, the greatest perfect square on this list is 12100 and the square root of 12100 is 110. Therefore, A equals 110.

B = Calculate 72600 divided by the greatest perfect square from the list of all factors of 72600. We determined above that the greatest perfect square from the list of all factors of 72600 is 12100. Furthermore, 72600 divided by 12100 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 72600 in its simplest radical form as follows:

√72600 = A√B

√72600 = 110√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72600 to simplify the square root of 72600 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 72600 and then take the square root of that product. The prime factors that multiply together to make 72600 are 2 x 2 x 2 x 3 x 5 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 11 x 11 = 12100 and the square root of 12100 is 110. Therefore, A equals 110.

B = Divide 72600 by the number (A) squared. 110 squared is 12100 and 72600 divided by 12100 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 72600 in its simplest radical form as follows:

√72600 = A√B

√72600 = 110√6

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

Simplify Square Root of 72601
Here is the next square root on our list that we have simplifed for you.