Simplify Square Root of 39762

Here we will show you two methods that you can use to simplify the square root of 39762. In other words, we will show you how to find the square root of 39762 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.

√39762 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39762 to simplify the square root of 39762. 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 39762. The factors of 39762 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 2209, 4418, 6627, 13254, 19881, and 39762. Furthermore, the greatest perfect square on this list is 19881 and the square root of 19881 is 141. Therefore, A equals 141.

B = Calculate 39762 divided by the greatest perfect square from the list of all factors of 39762. We determined above that the greatest perfect square from the list of all factors of 39762 is 19881. Furthermore, 39762 divided by 19881 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 39762 in its simplest radical form as follows:

√39762 = A√B

√39762 = 141√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39762 to simplify the square root of 39762 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 39762 and then take the square root of that product. The prime factors that multiply together to make 39762 are 2 x 3 x 3 x 47 x 47. When we strip out the pairs only, we get 3 x 3 x 47 x 47 = 19881 and the square root of 19881 is 141. Therefore, A equals 141.

B = Divide 39762 by the number (A) squared. 141 squared is 19881 and 39762 divided by 19881 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 39762 in its simplest radical form as follows:

√39762 = A√B

√39762 = 141√2

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Simplify Square Root of 39763
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