Simplify Square Root of 37905

Here we will show you two methods that you can use to simplify the square root of 37905. In other words, we will show you how to find the square root of 37905 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.

√37905 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37905 to simplify the square root of 37905. 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 37905. The factors of 37905 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 361, 399, 665, 1083, 1805, 1995, 2527, 5415, 7581, 12635, and 37905. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 37905 divided by the greatest perfect square from the list of all factors of 37905. We determined above that the greatest perfect square from the list of all factors of 37905 is 361. Furthermore, 37905 divided by 361 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 37905 in its simplest radical form as follows:

√37905 = A√B

√37905 = 19√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37905 to simplify the square root of 37905 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 37905 and then take the square root of that product. The prime factors that multiply together to make 37905 are 3 x 5 x 7 x 19 x 19. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 37905 by the number (A) squared. 19 squared is 361 and 37905 divided by 361 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 37905 in its simplest radical form as follows:

√37905 = A√B

√37905 = 19√105

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Simplify Square Root of 37906
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