Simplify Square Root of 39675

Here we will show you two methods that you can use to simplify the square root of 39675. In other words, we will show you how to find the square root of 39675 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.

√39675 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39675 to simplify the square root of 39675. 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 39675. The factors of 39675 are 1, 3, 5, 15, 23, 25, 69, 75, 115, 345, 529, 575, 1587, 1725, 2645, 7935, 13225, and 39675. Furthermore, the greatest perfect square on this list is 13225 and the square root of 13225 is 115. Therefore, A equals 115.

B = Calculate 39675 divided by the greatest perfect square from the list of all factors of 39675. We determined above that the greatest perfect square from the list of all factors of 39675 is 13225. Furthermore, 39675 divided by 13225 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 39675 in its simplest radical form as follows:

√39675 = A√B

√39675 = 115√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39675 to simplify the square root of 39675 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 39675 and then take the square root of that product. The prime factors that multiply together to make 39675 are 3 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 39675 by the number (A) squared. 115 squared is 13225 and 39675 divided by 13225 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 39675 in its simplest radical form as follows:

√39675 = A√B

√39675 = 115√3

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Simplify Square Root of 39676
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