Simplify Square Root of 39475

Here we will show you two methods that you can use to simplify the square root of 39475. In other words, we will show you how to find the square root of 39475 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.

√39475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39475 to simplify the square root of 39475. 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 39475. The factors of 39475 are 1, 5, 25, 1579, 7895, and 39475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 39475 divided by the greatest perfect square from the list of all factors of 39475. We determined above that the greatest perfect square from the list of all factors of 39475 is 25. Furthermore, 39475 divided by 25 is 1579, therefore B equals 1579.

Now we have A and B and can get our answer to 39475 in its simplest radical form as follows:

√39475 = A√B

√39475 = 5√1579

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39475 to simplify the square root of 39475 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 39475 and then take the square root of that product. The prime factors that multiply together to make 39475 are 5 x 5 x 1579. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 39475 by the number (A) squared. 5 squared is 25 and 39475 divided by 25 is 1579. Therefore, B equals 1579.

Once again we have A and B and can get our answer to 39475 in its simplest radical form as follows:

√39475 = A√B

√39475 = 5√1579

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Simplify Square Root of 39476
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