Simplify Square Root of 38332

Here we will show you two methods that you can use to simplify the square root of 38332. In other words, we will show you how to find the square root of 38332 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.

√38332 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38332 to simplify the square root of 38332. 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 38332. The factors of 38332 are 1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518, 1036, 1369, 2738, 5476, 9583, 19166, and 38332. Furthermore, the greatest perfect square on this list is 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Calculate 38332 divided by the greatest perfect square from the list of all factors of 38332. We determined above that the greatest perfect square from the list of all factors of 38332 is 5476. Furthermore, 38332 divided by 5476 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 38332 in its simplest radical form as follows:

√38332 = A√B

√38332 = 74√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38332 to simplify the square root of 38332 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 38332 and then take the square root of that product. The prime factors that multiply together to make 38332 are 2 x 2 x 7 x 37 x 37. When we strip out the pairs only, we get 2 x 2 x 37 x 37 = 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Divide 38332 by the number (A) squared. 74 squared is 5476 and 38332 divided by 5476 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 38332 in its simplest radical form as follows:

√38332 = A√B

√38332 = 74√7

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Simplify Square Root of 38333
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