Simplify Square Root of 40898

Here we will show you two methods that you can use to simplify the square root of 40898. In other words, we will show you how to find the square root of 40898 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.

√40898 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40898 to simplify the square root of 40898. 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 40898. The factors of 40898 are 1, 2, 11, 13, 22, 26, 121, 143, 169, 242, 286, 338, 1573, 1859, 3146, 3718, 20449, and 40898. Furthermore, the greatest perfect square on this list is 20449 and the square root of 20449 is 143. Therefore, A equals 143.

B = Calculate 40898 divided by the greatest perfect square from the list of all factors of 40898. We determined above that the greatest perfect square from the list of all factors of 40898 is 20449. Furthermore, 40898 divided by 20449 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 40898 in its simplest radical form as follows:

√40898 = A√B

√40898 = 143√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40898 to simplify the square root of 40898 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 40898 and then take the square root of that product. The prime factors that multiply together to make 40898 are 2 x 11 x 11 x 13 x 13. When we strip out the pairs only, we get 11 x 11 x 13 x 13 = 20449 and the square root of 20449 is 143. Therefore, A equals 143.

B = Divide 40898 by the number (A) squared. 143 squared is 20449 and 40898 divided by 20449 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 40898 in its simplest radical form as follows:

√40898 = A√B

√40898 = 143√2

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