Simplify Square Root of 46359

Here we will show you two methods that you can use to simplify the square root of 46359. In other words, we will show you how to find the square root of 46359 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.

√46359 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46359 to simplify the square root of 46359. 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 46359. The factors of 46359 are 1, 3, 9, 17, 27, 51, 101, 153, 303, 459, 909, 1717, 2727, 5151, 15453, and 46359. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 46359 divided by the greatest perfect square from the list of all factors of 46359. We determined above that the greatest perfect square from the list of all factors of 46359 is 9. Furthermore, 46359 divided by 9 is 5151, therefore B equals 5151.

Now we have A and B and can get our answer to 46359 in its simplest radical form as follows:

√46359 = A√B

√46359 = 3√5151

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46359 to simplify the square root of 46359 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 46359 and then take the square root of that product. The prime factors that multiply together to make 46359 are 3 x 3 x 3 x 17 x 101. 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 46359 by the number (A) squared. 3 squared is 9 and 46359 divided by 9 is 5151. Therefore, B equals 5151.

Once again we have A and B and can get our answer to 46359 in its simplest radical form as follows:

√46359 = A√B

√46359 = 3√5151

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