Simplify Square Root of 37856

Here we will show you two methods that you can use to simplify the square root of 37856. In other words, we will show you how to find the square root of 37856 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.

√37856 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37856 to simplify the square root of 37856. 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 37856. The factors of 37856 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 676, 728, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 9464, 18928, and 37856. Furthermore, the greatest perfect square on this list is 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Calculate 37856 divided by the greatest perfect square from the list of all factors of 37856. We determined above that the greatest perfect square from the list of all factors of 37856 is 2704. Furthermore, 37856 divided by 2704 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 37856 in its simplest radical form as follows:

√37856 = A√B

√37856 = 52√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37856 to simplify the square root of 37856 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 37856 and then take the square root of that product. The prime factors that multiply together to make 37856 are 2 x 2 x 2 x 2 x 2 x 7 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 13 x 13 = 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Divide 37856 by the number (A) squared. 52 squared is 2704 and 37856 divided by 2704 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 37856 in its simplest radical form as follows:

√37856 = A√B

√37856 = 52√14

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