Simplify Square Root of 73125

Here we will show you two methods that you can use to simplify the square root of 73125. In other words, we will show you how to find the square root of 73125 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.

√73125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73125 to simplify the square root of 73125. 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 73125. The factors of 73125 are 1, 3, 5, 9, 13, 15, 25, 39, 45, 65, 75, 117, 125, 195, 225, 325, 375, 585, 625, 975, 1125, 1625, 1875, 2925, 4875, 5625, 8125, 14625, 24375, and 73125. Furthermore, the greatest perfect square on this list is 5625 and the square root of 5625 is 75. Therefore, A equals 75.

B = Calculate 73125 divided by the greatest perfect square from the list of all factors of 73125. We determined above that the greatest perfect square from the list of all factors of 73125 is 5625. Furthermore, 73125 divided by 5625 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 73125 in its simplest radical form as follows:

√73125 = A√B

√73125 = 75√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73125 to simplify the square root of 73125 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 73125 and then take the square root of that product. The prime factors that multiply together to make 73125 are 3 x 3 x 5 x 5 x 5 x 5 x 13. When we strip out the pairs only, we get 3 x 3 x 5 x 5 x 5 x 5 = 5625 and the square root of 5625 is 75. Therefore, A equals 75.

B = Divide 73125 by the number (A) squared. 75 squared is 5625 and 73125 divided by 5625 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 73125 in its simplest radical form as follows:

√73125 = A√B

√73125 = 75√13

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Simplify Square Root of 73126
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