Simplify Square Root of 87171

Here we will show you two methods that you can use to simplify the square root of 87171. In other words, we will show you how to find the square root of 87171 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.

√87171 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87171 to simplify the square root of 87171. 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 87171. The factors of 87171 are 1, 3, 7, 21, 49, 147, 593, 1779, 4151, 12453, 29057, and 87171. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 87171 divided by the greatest perfect square from the list of all factors of 87171. We determined above that the greatest perfect square from the list of all factors of 87171 is 49. Furthermore, 87171 divided by 49 is 1779, therefore B equals 1779.

Now we have A and B and can get our answer to 87171 in its simplest radical form as follows:

√87171 = A√B

√87171 = 7√1779

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87171 to simplify the square root of 87171 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 87171 and then take the square root of that product. The prime factors that multiply together to make 87171 are 3 x 7 x 7 x 593. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 87171 by the number (A) squared. 7 squared is 49 and 87171 divided by 49 is 1779. Therefore, B equals 1779.

Once again we have A and B and can get our answer to 87171 in its simplest radical form as follows:

√87171 = A√B

√87171 = 7√1779

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Simplify Square Root of 87172
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