Simplify Square Root of 39775

Here we will show you two methods that you can use to simplify the square root of 39775. In other words, we will show you how to find the square root of 39775 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.

√39775 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39775 to simplify the square root of 39775. 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 39775. The factors of 39775 are 1, 5, 25, 37, 43, 185, 215, 925, 1075, 1591, 7955, and 39775. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 39775 divided by the greatest perfect square from the list of all factors of 39775. We determined above that the greatest perfect square from the list of all factors of 39775 is 25. Furthermore, 39775 divided by 25 is 1591, therefore B equals 1591.

Now we have A and B and can get our answer to 39775 in its simplest radical form as follows:

√39775 = A√B

√39775 = 5√1591

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39775 to simplify the square root of 39775 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 39775 and then take the square root of that product. The prime factors that multiply together to make 39775 are 5 x 5 x 37 x 43. 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 39775 by the number (A) squared. 5 squared is 25 and 39775 divided by 25 is 1591. Therefore, B equals 1591.

Once again we have A and B and can get our answer to 39775 in its simplest radical form as follows:

√39775 = A√B

√39775 = 5√1591

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Simplify Square Root of 39776
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