Simplify Square Root of 89528

Here we will show you two methods that you can use to simplify the square root of 89528. In other words, we will show you how to find the square root of 89528 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.

√89528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89528 to simplify the square root of 89528. 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 89528. The factors of 89528 are 1, 2, 4, 8, 19, 31, 38, 62, 76, 124, 152, 248, 361, 589, 722, 1178, 1444, 2356, 2888, 4712, 11191, 22382, 44764, and 89528. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 89528 divided by the greatest perfect square from the list of all factors of 89528. We determined above that the greatest perfect square from the list of all factors of 89528 is 1444. Furthermore, 89528 divided by 1444 is 62, therefore B equals 62.

Now we have A and B and can get our answer to 89528 in its simplest radical form as follows:

√89528 = A√B

√89528 = 38√62

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89528 to simplify the square root of 89528 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 89528 and then take the square root of that product. The prime factors that multiply together to make 89528 are 2 x 2 x 2 x 19 x 19 x 31. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 89528 by the number (A) squared. 38 squared is 1444 and 89528 divided by 1444 is 62. Therefore, B equals 62.

Once again we have A and B and can get our answer to 89528 in its simplest radical form as follows:

√89528 = A√B

√89528 = 38√62

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