Simplify Square Root of 46813

Here we will show you two methods that you can use to simplify the square root of 46813. In other words, we will show you how to find the square root of 46813 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.

√46813 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46813 to simplify the square root of 46813. 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 46813. The factors of 46813 are 1, 13, 169, 277, 3601, and 46813. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 46813 divided by the greatest perfect square from the list of all factors of 46813. We determined above that the greatest perfect square from the list of all factors of 46813 is 169. Furthermore, 46813 divided by 169 is 277, therefore B equals 277.

Now we have A and B and can get our answer to 46813 in its simplest radical form as follows:

√46813 = A√B

√46813 = 13√277

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46813 to simplify the square root of 46813 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 46813 and then take the square root of that product. The prime factors that multiply together to make 46813 are 13 x 13 x 277. 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 46813 by the number (A) squared. 13 squared is 169 and 46813 divided by 169 is 277. Therefore, B equals 277.

Once again we have A and B and can get our answer to 46813 in its simplest radical form as follows:

√46813 = A√B

√46813 = 13√277

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Simplify Square Root of 46814
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