Simplify Square Root of 89536

Here we will show you two methods that you can use to simplify the square root of 89536. In other words, we will show you how to find the square root of 89536 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.

√89536 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89536 to simplify the square root of 89536. 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 89536. The factors of 89536 are 1, 2, 4, 8, 16, 32, 64, 1399, 2798, 5596, 11192, 22384, 44768, and 89536. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 89536 divided by the greatest perfect square from the list of all factors of 89536. We determined above that the greatest perfect square from the list of all factors of 89536 is 64. Furthermore, 89536 divided by 64 is 1399, therefore B equals 1399.

Now we have A and B and can get our answer to 89536 in its simplest radical form as follows:

√89536 = A√B

√89536 = 8√1399

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89536 to simplify the square root of 89536 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 89536 and then take the square root of that product. The prime factors that multiply together to make 89536 are 2 x 2 x 2 x 2 x 2 x 2 x 1399. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 89536 by the number (A) squared. 8 squared is 64 and 89536 divided by 64 is 1399. Therefore, B equals 1399.

Once again we have A and B and can get our answer to 89536 in its simplest radical form as follows:

√89536 = A√B

√89536 = 8√1399

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Simplify Square Root of 89537
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