Simplify Square Root of 46818

Here we will show you two methods that you can use to simplify the square root of 46818. In other words, we will show you how to find the square root of 46818 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.

√46818 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 46818 to simplify the square root of 46818. 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 46818. The factors of 46818 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 81, 102, 153, 162, 289, 306, 459, 578, 867, 918, 1377, 1734, 2601, 2754, 5202, 7803, 15606, 23409, and 46818. Furthermore, the greatest perfect square on this list is 23409 and the square root of 23409 is 153. Therefore, A equals 153.

B = Calculate 46818 divided by the greatest perfect square from the list of all factors of 46818. We determined above that the greatest perfect square from the list of all factors of 46818 is 23409. Furthermore, 46818 divided by 23409 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 46818 in its simplest radical form as follows:

√46818 = A√B

√46818 = 153√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 46818 to simplify the square root of 46818 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 46818 and then take the square root of that product. The prime factors that multiply together to make 46818 are 2 x 3 x 3 x 3 x 3 x 17 x 17. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 17 x 17 = 23409 and the square root of 23409 is 153. Therefore, A equals 153.

B = Divide 46818 by the number (A) squared. 153 squared is 23409 and 46818 divided by 23409 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 46818 in its simplest radical form as follows:

√46818 = A√B

√46818 = 153√2

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