Simplify Square Root of 39825

Here we will show you two methods that you can use to simplify the square root of 39825. In other words, we will show you how to find the square root of 39825 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.

√39825 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39825 to simplify the square root of 39825. 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 39825. The factors of 39825 are 1, 3, 5, 9, 15, 25, 27, 45, 59, 75, 135, 177, 225, 295, 531, 675, 885, 1475, 1593, 2655, 4425, 7965, 13275, and 39825. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 39825 divided by the greatest perfect square from the list of all factors of 39825. We determined above that the greatest perfect square from the list of all factors of 39825 is 225. Furthermore, 39825 divided by 225 is 177, therefore B equals 177.

Now we have A and B and can get our answer to 39825 in its simplest radical form as follows:

√39825 = A√B

√39825 = 15√177

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39825 to simplify the square root of 39825 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 39825 and then take the square root of that product. The prime factors that multiply together to make 39825 are 3 x 3 x 3 x 5 x 5 x 59. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 39825 by the number (A) squared. 15 squared is 225 and 39825 divided by 225 is 177. Therefore, B equals 177.

Once again we have A and B and can get our answer to 39825 in its simplest radical form as follows:

√39825 = A√B

√39825 = 15√177

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Simplify Square Root of 39826
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