Simplify Square Root of 39605

Here we will show you two methods that you can use to simplify the square root of 39605. In other words, we will show you how to find the square root of 39605 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.

√39605 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39605 to simplify the square root of 39605. 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 39605. The factors of 39605 are 1, 5, 89, 445, 7921, and 39605. Furthermore, the greatest perfect square on this list is 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Calculate 39605 divided by the greatest perfect square from the list of all factors of 39605. We determined above that the greatest perfect square from the list of all factors of 39605 is 7921. Furthermore, 39605 divided by 7921 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 39605 in its simplest radical form as follows:

√39605 = A√B

√39605 = 89√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39605 to simplify the square root of 39605 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 39605 and then take the square root of that product. The prime factors that multiply together to make 39605 are 5 x 89 x 89. When we strip out the pairs only, we get 89 x 89 = 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Divide 39605 by the number (A) squared. 89 squared is 7921 and 39605 divided by 7921 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 39605 in its simplest radical form as follows:

√39605 = A√B

√39605 = 89√5

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Simplify Square Root of 39606
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