Simplify Square Root of 89475

Here we will show you two methods that you can use to simplify the square root of 89475. In other words, we will show you how to find the square root of 89475 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.

√89475 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89475 to simplify the square root of 89475. 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 89475. The factors of 89475 are 1, 3, 5, 15, 25, 75, 1193, 3579, 5965, 17895, 29825, and 89475. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 89475 divided by the greatest perfect square from the list of all factors of 89475. We determined above that the greatest perfect square from the list of all factors of 89475 is 25. Furthermore, 89475 divided by 25 is 3579, therefore B equals 3579.

Now we have A and B and can get our answer to 89475 in its simplest radical form as follows:

√89475 = A√B

√89475 = 5√3579

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89475 to simplify the square root of 89475 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 89475 and then take the square root of that product. The prime factors that multiply together to make 89475 are 3 x 5 x 5 x 1193. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 89475 by the number (A) squared. 5 squared is 25 and 89475 divided by 25 is 3579. Therefore, B equals 3579.

Once again we have A and B and can get our answer to 89475 in its simplest radical form as follows:

√89475 = A√B

√89475 = 5√3579

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Simplify Square Root of 89476
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