Simplify Square Root of 75988

Here we will show you two methods that you can use to simplify the square root of 75988. In other words, we will show you how to find the square root of 75988 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.

√75988 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75988 to simplify the square root of 75988. 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 75988. The factors of 75988 are 1, 2, 4, 11, 22, 44, 121, 157, 242, 314, 484, 628, 1727, 3454, 6908, 18997, 37994, and 75988. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 75988 divided by the greatest perfect square from the list of all factors of 75988. We determined above that the greatest perfect square from the list of all factors of 75988 is 484. Furthermore, 75988 divided by 484 is 157, therefore B equals 157.

Now we have A and B and can get our answer to 75988 in its simplest radical form as follows:

√75988 = A√B

√75988 = 22√157

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75988 to simplify the square root of 75988 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 75988 and then take the square root of that product. The prime factors that multiply together to make 75988 are 2 x 2 x 11 x 11 x 157. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 75988 by the number (A) squared. 22 squared is 484 and 75988 divided by 484 is 157. Therefore, B equals 157.

Once again we have A and B and can get our answer to 75988 in its simplest radical form as follows:

√75988 = A√B

√75988 = 22√157

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Simplify Square Root of 75989
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