Simplify Square Root of 39882

Here we will show you two methods that you can use to simplify the square root of 39882. In other words, we will show you how to find the square root of 39882 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.

√39882 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39882 to simplify the square root of 39882. 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 39882. The factors of 39882 are 1, 2, 3, 6, 17, 23, 34, 46, 51, 69, 102, 138, 289, 391, 578, 782, 867, 1173, 1734, 2346, 6647, 13294, 19941, and 39882. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 39882 divided by the greatest perfect square from the list of all factors of 39882. We determined above that the greatest perfect square from the list of all factors of 39882 is 289. Furthermore, 39882 divided by 289 is 138, therefore B equals 138.

Now we have A and B and can get our answer to 39882 in its simplest radical form as follows:

√39882 = A√B

√39882 = 17√138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39882 to simplify the square root of 39882 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 39882 and then take the square root of that product. The prime factors that multiply together to make 39882 are 2 x 3 x 17 x 17 x 23. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 39882 by the number (A) squared. 17 squared is 289 and 39882 divided by 289 is 138. Therefore, B equals 138.

Once again we have A and B and can get our answer to 39882 in its simplest radical form as follows:

√39882 = A√B

√39882 = 17√138

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Simplify Square Root of 39883
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