Simplify Square Root of 7600

Here we will show you two methods that you can use to simplify the square root of 7600. In other words, we will show you how to find the square root of 7600 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.

√7600 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7600 to simplify the square root of 7600. 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 7600. The factors of 7600 are 1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 38, 40, 50, 76, 80, 95, 100, 152, 190, 200, 304, 380, 400, 475, 760, 950, 1520, 1900, 3800, and 7600. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 7600 divided by the greatest perfect square from the list of all factors of 7600. We determined above that the greatest perfect square from the list of all factors of 7600 is 400. Furthermore, 7600 divided by 400 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 7600 in its simplest radical form as follows:

√7600 = A√B

√7600 = 20√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7600 to simplify the square root of 7600 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 7600 and then take the square root of that product. The prime factors that multiply together to make 7600 are 2 x 2 x 2 x 2 x 5 x 5 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 7600 by the number (A) squared. 20 squared is 400 and 7600 divided by 400 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 7600 in its simplest radical form as follows:

√7600 = A√B

√7600 = 20√19

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