Simplify Square Root of 88344

Here we will show you two methods that you can use to simplify the square root of 88344. In other words, we will show you how to find the square root of 88344 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.

√88344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88344 to simplify the square root of 88344. 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 88344. The factors of 88344 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 409, 818, 1227, 1636, 2454, 3272, 3681, 4908, 7362, 9816, 11043, 14724, 22086, 29448, 44172, and 88344. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 88344 divided by the greatest perfect square from the list of all factors of 88344. We determined above that the greatest perfect square from the list of all factors of 88344 is 36. Furthermore, 88344 divided by 36 is 2454, therefore B equals 2454.

Now we have A and B and can get our answer to 88344 in its simplest radical form as follows:

√88344 = A√B

√88344 = 6√2454

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88344 to simplify the square root of 88344 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 88344 and then take the square root of that product. The prime factors that multiply together to make 88344 are 2 x 2 x 2 x 3 x 3 x 3 x 409. 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 88344 by the number (A) squared. 6 squared is 36 and 88344 divided by 36 is 2454. Therefore, B equals 2454.

Once again we have A and B and can get our answer to 88344 in its simplest radical form as follows:

√88344 = A√B

√88344 = 6√2454

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