Simplify Square Root of 37538

Here we will show you two methods that you can use to simplify the square root of 37538. In other words, we will show you how to find the square root of 37538 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.

√37538 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37538 to simplify the square root of 37538. 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 37538. The factors of 37538 are 1, 2, 137, 274, 18769, and 37538. Furthermore, the greatest perfect square on this list is 18769 and the square root of 18769 is 137. Therefore, A equals 137.

B = Calculate 37538 divided by the greatest perfect square from the list of all factors of 37538. We determined above that the greatest perfect square from the list of all factors of 37538 is 18769. Furthermore, 37538 divided by 18769 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 37538 in its simplest radical form as follows:

√37538 = A√B

√37538 = 137√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37538 to simplify the square root of 37538 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 37538 and then take the square root of that product. The prime factors that multiply together to make 37538 are 2 x 137 x 137. When we strip out the pairs only, we get 137 x 137 = 18769 and the square root of 18769 is 137. Therefore, A equals 137.

B = Divide 37538 by the number (A) squared. 137 squared is 18769 and 37538 divided by 18769 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 37538 in its simplest radical form as follows:

√37538 = A√B

√37538 = 137√2

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Simplify Square Root of 37539
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