Simplify Square Root of 35321

Here we will show you two methods that you can use to simplify the square root of 35321. In other words, we will show you how to find the square root of 35321 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.

√35321 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35321 to simplify the square root of 35321. 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 35321. The factors of 35321 are 1, 11, 13, 19, 143, 169, 209, 247, 1859, 2717, 3211, and 35321. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 35321 divided by the greatest perfect square from the list of all factors of 35321. We determined above that the greatest perfect square from the list of all factors of 35321 is 169. Furthermore, 35321 divided by 169 is 209, therefore B equals 209.

Now we have A and B and can get our answer to 35321 in its simplest radical form as follows:

√35321 = A√B

√35321 = 13√209

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35321 to simplify the square root of 35321 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 35321 and then take the square root of that product. The prime factors that multiply together to make 35321 are 11 x 13 x 13 x 19. 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 35321 by the number (A) squared. 13 squared is 169 and 35321 divided by 169 is 209. Therefore, B equals 209.

Once again we have A and B and can get our answer to 35321 in its simplest radical form as follows:

√35321 = A√B

√35321 = 13√209

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Simplify Square Root of 35322
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