Simplify Square Root of 46456

Here we will show you two methods that you can use to simplify the square root of 46456. In other words, we will show you how to find the square root of 46456 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.

√46456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46456 to simplify the square root of 46456. 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 46456. The factors of 46456 are 1, 2, 4, 8, 5807, 11614, 23228, and 46456. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 46456 divided by the greatest perfect square from the list of all factors of 46456. We determined above that the greatest perfect square from the list of all factors of 46456 is 4. Furthermore, 46456 divided by 4 is 11614, therefore B equals 11614.

Now we have A and B and can get our answer to 46456 in its simplest radical form as follows:

√46456 = A√B

√46456 = 2√11614

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46456 to simplify the square root of 46456 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 46456 and then take the square root of that product. The prime factors that multiply together to make 46456 are 2 x 2 x 2 x 5807. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 46456 by the number (A) squared. 2 squared is 4 and 46456 divided by 4 is 11614. Therefore, B equals 11614.

Once again we have A and B and can get our answer to 46456 in its simplest radical form as follows:

√46456 = A√B

√46456 = 2√11614

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Simplify Square Root of 46457
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