Simplify Square Root of 87660

Here we will show you two methods that you can use to simplify the square root of 87660. In other words, we will show you how to find the square root of 87660 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.

√87660 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87660 to simplify the square root of 87660. 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 87660. The factors of 87660 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 487, 974, 1461, 1948, 2435, 2922, 4383, 4870, 5844, 7305, 8766, 9740, 14610, 17532, 21915, 29220, 43830, and 87660. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 87660 divided by the greatest perfect square from the list of all factors of 87660. We determined above that the greatest perfect square from the list of all factors of 87660 is 36. Furthermore, 87660 divided by 36 is 2435, therefore B equals 2435.

Now we have A and B and can get our answer to 87660 in its simplest radical form as follows:

√87660 = A√B

√87660 = 6√2435

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87660 to simplify the square root of 87660 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 87660 and then take the square root of that product. The prime factors that multiply together to make 87660 are 2 x 2 x 3 x 3 x 5 x 487. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 87660 by the number (A) squared. 6 squared is 36 and 87660 divided by 36 is 2435. Therefore, B equals 2435.

Once again we have A and B and can get our answer to 87660 in its simplest radical form as follows:

√87660 = A√B

√87660 = 6√2435

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