Simplify Square Root of 24500

Here we will show you two methods that you can use to simplify the square root of 24500. In other words, we will show you how to find the square root of 24500 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.

√24500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24500 to simplify the square root of 24500. 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 24500. The factors of 24500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 125, 140, 175, 196, 245, 250, 350, 490, 500, 700, 875, 980, 1225, 1750, 2450, 3500, 4900, 6125, 12250, and 24500. Furthermore, the greatest perfect square on this list is 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Calculate 24500 divided by the greatest perfect square from the list of all factors of 24500. We determined above that the greatest perfect square from the list of all factors of 24500 is 4900. Furthermore, 24500 divided by 4900 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 24500 in its simplest radical form as follows:

√24500 = A√B

√24500 = 70√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24500 to simplify the square root of 24500 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 24500 and then take the square root of that product. The prime factors that multiply together to make 24500 are 2 x 2 x 5 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 7 x 7 = 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Divide 24500 by the number (A) squared. 70 squared is 4900 and 24500 divided by 4900 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 24500 in its simplest radical form as follows:

√24500 = A√B

√24500 = 70√5

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

Simplify Square Root of 24501
Here is the next square root on our list that we have simplifed for you.