Simplify Square Root of 66125

Here we will show you two methods that you can use to simplify the square root of 66125. In other words, we will show you how to find the square root of 66125 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.

√66125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66125 to simplify the square root of 66125. 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 66125. The factors of 66125 are 1, 5, 23, 25, 115, 125, 529, 575, 2645, 2875, 13225, and 66125. Furthermore, the greatest perfect square on this list is 13225 and the square root of 13225 is 115. Therefore, A equals 115.

B = Calculate 66125 divided by the greatest perfect square from the list of all factors of 66125. We determined above that the greatest perfect square from the list of all factors of 66125 is 13225. Furthermore, 66125 divided by 13225 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 66125 in its simplest radical form as follows:

√66125 = A√B

√66125 = 115√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66125 to simplify the square root of 66125 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 66125 and then take the square root of that product. The prime factors that multiply together to make 66125 are 5 x 5 x 5 x 23 x 23. When we strip out the pairs only, we get 5 x 5 x 23 x 23 = 13225 and the square root of 13225 is 115. Therefore, A equals 115.

B = Divide 66125 by the number (A) squared. 115 squared is 13225 and 66125 divided by 13225 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 66125 in its simplest radical form as follows:

√66125 = A√B

√66125 = 115√5

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Simplify Square Root of 66126
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