Simplify Square Root of 87723

Here we will show you two methods that you can use to simplify the square root of 87723. In other words, we will show you how to find the square root of 87723 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.

√87723 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87723 to simplify the square root of 87723. 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 87723. The factors of 87723 are 1, 3, 9, 19, 27, 57, 81, 171, 243, 361, 513, 1083, 1539, 3249, 4617, 9747, 29241, and 87723. Furthermore, the greatest perfect square on this list is 29241 and the square root of 29241 is 171. Therefore, A equals 171.

B = Calculate 87723 divided by the greatest perfect square from the list of all factors of 87723. We determined above that the greatest perfect square from the list of all factors of 87723 is 29241. Furthermore, 87723 divided by 29241 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 87723 in its simplest radical form as follows:

√87723 = A√B

√87723 = 171√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87723 to simplify the square root of 87723 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 87723 and then take the square root of that product. The prime factors that multiply together to make 87723 are 3 x 3 x 3 x 3 x 3 x 19 x 19. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 19 x 19 = 29241 and the square root of 29241 is 171. Therefore, A equals 171.

B = Divide 87723 by the number (A) squared. 171 squared is 29241 and 87723 divided by 29241 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 87723 in its simplest radical form as follows:

√87723 = A√B

√87723 = 171√3

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Simplify Square Root of 87724
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