Simplify Square Root of 37700

Here we will show you two methods that you can use to simplify the square root of 37700. In other words, we will show you how to find the square root of 37700 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.

√37700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37700 to simplify the square root of 37700. 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 37700. The factors of 37700 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 29, 50, 52, 58, 65, 100, 116, 130, 145, 260, 290, 325, 377, 580, 650, 725, 754, 1300, 1450, 1508, 1885, 2900, 3770, 7540, 9425, 18850, and 37700. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 37700 divided by the greatest perfect square from the list of all factors of 37700. We determined above that the greatest perfect square from the list of all factors of 37700 is 100. Furthermore, 37700 divided by 100 is 377, therefore B equals 377.

Now we have A and B and can get our answer to 37700 in its simplest radical form as follows:

√37700 = A√B

√37700 = 10√377

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37700 to simplify the square root of 37700 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 37700 and then take the square root of that product. The prime factors that multiply together to make 37700 are 2 x 2 x 5 x 5 x 13 x 29. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 37700 by the number (A) squared. 10 squared is 100 and 37700 divided by 100 is 377. Therefore, B equals 377.

Once again we have A and B and can get our answer to 37700 in its simplest radical form as follows:

√37700 = A√B

√37700 = 10√377

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