Simplify Square Root of 7500

Here we will show you two methods that you can use to simplify the square root of 7500. In other words, we will show you how to find the square root of 7500 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.

√7500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7500 to simplify the square root of 7500. 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 7500. The factors of 7500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 625, 750, 1250, 1500, 1875, 2500, 3750, and 7500. Furthermore, the greatest perfect square on this list is 2500 and the square root of 2500 is 50. Therefore, A equals 50.

B = Calculate 7500 divided by the greatest perfect square from the list of all factors of 7500. We determined above that the greatest perfect square from the list of all factors of 7500 is 2500. Furthermore, 7500 divided by 2500 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 7500 in its simplest radical form as follows:

√7500 = A√B

√7500 = 50√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7500 to simplify the square root of 7500 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 7500 and then take the square root of that product. The prime factors that multiply together to make 7500 are 2 x 2 x 3 x 5 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 5 x 5 = 2500 and the square root of 2500 is 50. Therefore, A equals 50.

B = Divide 7500 by the number (A) squared. 50 squared is 2500 and 7500 divided by 2500 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 7500 in its simplest radical form as follows:

√7500 = A√B

√7500 = 50√3

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