Simplify Square Root of 7688

Here we will show you two methods that you can use to simplify the square root of 7688. In other words, we will show you how to find the square root of 7688 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.

√7688 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7688 to simplify the square root of 7688. 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 7688. The factors of 7688 are 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, and 7688. Furthermore, the greatest perfect square on this list is 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Calculate 7688 divided by the greatest perfect square from the list of all factors of 7688. We determined above that the greatest perfect square from the list of all factors of 7688 is 3844. Furthermore, 7688 divided by 3844 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 7688 in its simplest radical form as follows:

√7688 = A√B

√7688 = 62√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7688 to simplify the square root of 7688 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 7688 and then take the square root of that product. The prime factors that multiply together to make 7688 are 2 x 2 x 2 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 31 x 31 = 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Divide 7688 by the number (A) squared. 62 squared is 3844 and 7688 divided by 3844 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 7688 in its simplest radical form as follows:

√7688 = A√B

√7688 = 62√2

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Simplify Square Root of 7689
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