Simplify Square Root of 64389

Here we will show you two methods that you can use to simplify the square root of 64389. In other words, we will show you how to find the square root of 64389 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.

√64389 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64389 to simplify the square root of 64389. 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 64389. The factors of 64389 are 1, 3, 13, 39, 127, 169, 381, 507, 1651, 4953, 21463, and 64389. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 64389 divided by the greatest perfect square from the list of all factors of 64389. We determined above that the greatest perfect square from the list of all factors of 64389 is 169. Furthermore, 64389 divided by 169 is 381, therefore B equals 381.

Now we have A and B and can get our answer to 64389 in its simplest radical form as follows:

√64389 = A√B

√64389 = 13√381

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64389 to simplify the square root of 64389 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 64389 and then take the square root of that product. The prime factors that multiply together to make 64389 are 3 x 13 x 13 x 127. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 64389 by the number (A) squared. 13 squared is 169 and 64389 divided by 169 is 381. Therefore, B equals 381.

Once again we have A and B and can get our answer to 64389 in its simplest radical form as follows:

√64389 = A√B

√64389 = 13√381

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Simplify Square Root of 64390
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