Simplify Square Root of 39701

Here we will show you two methods that you can use to simplify the square root of 39701. In other words, we will show you how to find the square root of 39701 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.

√39701 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39701 to simplify the square root of 39701. 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 39701. The factors of 39701 are 1, 29, 37, 1073, 1369, and 39701. Furthermore, the greatest perfect square on this list is 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Calculate 39701 divided by the greatest perfect square from the list of all factors of 39701. We determined above that the greatest perfect square from the list of all factors of 39701 is 1369. Furthermore, 39701 divided by 1369 is 29, therefore B equals 29.

Now we have A and B and can get our answer to 39701 in its simplest radical form as follows:

√39701 = A√B

√39701 = 37√29

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39701 to simplify the square root of 39701 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 39701 and then take the square root of that product. The prime factors that multiply together to make 39701 are 29 x 37 x 37. When we strip out the pairs only, we get 37 x 37 = 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Divide 39701 by the number (A) squared. 37 squared is 1369 and 39701 divided by 1369 is 29. Therefore, B equals 29.

Once again we have A and B and can get our answer to 39701 in its simplest radical form as follows:

√39701 = A√B

√39701 = 37√29

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Simplify Square Root of 39702
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