Simplify Square Root of 87451

Here we will show you two methods that you can use to simplify the square root of 87451. In other words, we will show you how to find the square root of 87451 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.

√87451 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87451 to simplify the square root of 87451. 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 87451. The factors of 87451 are 1, 7, 13, 31, 91, 217, 403, 961, 2821, 6727, 12493, and 87451. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 87451 divided by the greatest perfect square from the list of all factors of 87451. We determined above that the greatest perfect square from the list of all factors of 87451 is 961. Furthermore, 87451 divided by 961 is 91, therefore B equals 91.

Now we have A and B and can get our answer to 87451 in its simplest radical form as follows:

√87451 = A√B

√87451 = 31√91

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87451 to simplify the square root of 87451 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 87451 and then take the square root of that product. The prime factors that multiply together to make 87451 are 7 x 13 x 31 x 31. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 87451 by the number (A) squared. 31 squared is 961 and 87451 divided by 961 is 91. Therefore, B equals 91.

Once again we have A and B and can get our answer to 87451 in its simplest radical form as follows:

√87451 = A√B

√87451 = 31√91

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Simplify Square Root of 87452
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