Simplify Square Root of 64395

Here we will show you two methods that you can use to simplify the square root of 64395. In other words, we will show you how to find the square root of 64395 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.

√64395 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64395 to simplify the square root of 64395. 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 64395. The factors of 64395 are 1, 3, 5, 9, 15, 27, 45, 53, 81, 135, 159, 243, 265, 405, 477, 795, 1215, 1431, 2385, 4293, 7155, 12879, 21465, and 64395. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 64395 divided by the greatest perfect square from the list of all factors of 64395. We determined above that the greatest perfect square from the list of all factors of 64395 is 81. Furthermore, 64395 divided by 81 is 795, therefore B equals 795.

Now we have A and B and can get our answer to 64395 in its simplest radical form as follows:

√64395 = A√B

√64395 = 9√795

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64395 to simplify the square root of 64395 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 64395 and then take the square root of that product. The prime factors that multiply together to make 64395 are 3 x 3 x 3 x 3 x 3 x 5 x 53. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 64395 by the number (A) squared. 9 squared is 81 and 64395 divided by 81 is 795. Therefore, B equals 795.

Once again we have A and B and can get our answer to 64395 in its simplest radical form as follows:

√64395 = A√B

√64395 = 9√795

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Simplify Square Root of 64396
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