Simplify Square Root of 85653

Here we will show you two methods that you can use to simplify the square root of 85653. In other words, we will show you how to find the square root of 85653 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.

√85653 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85653 to simplify the square root of 85653. 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 85653. The factors of 85653 are 1, 3, 9, 31, 93, 279, 307, 921, 2763, 9517, 28551, and 85653. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 85653 divided by the greatest perfect square from the list of all factors of 85653. We determined above that the greatest perfect square from the list of all factors of 85653 is 9. Furthermore, 85653 divided by 9 is 9517, therefore B equals 9517.

Now we have A and B and can get our answer to 85653 in its simplest radical form as follows:

√85653 = A√B

√85653 = 3√9517

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85653 to simplify the square root of 85653 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 85653 and then take the square root of that product. The prime factors that multiply together to make 85653 are 3 x 3 x 31 x 307. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 85653 by the number (A) squared. 3 squared is 9 and 85653 divided by 9 is 9517. Therefore, B equals 9517.

Once again we have A and B and can get our answer to 85653 in its simplest radical form as follows:

√85653 = A√B

√85653 = 3√9517

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Simplify Square Root of 85654
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