Simplify Square Root of 58643

Here we will show you two methods that you can use to simplify the square root of 58643. In other words, we will show you how to find the square root of 58643 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.

√58643 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58643 to simplify the square root of 58643. 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 58643. The factors of 58643 are 1, 13, 169, 347, 4511, and 58643. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 58643 divided by the greatest perfect square from the list of all factors of 58643. We determined above that the greatest perfect square from the list of all factors of 58643 is 169. Furthermore, 58643 divided by 169 is 347, therefore B equals 347.

Now we have A and B and can get our answer to 58643 in its simplest radical form as follows:

√58643 = A√B

√58643 = 13√347

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58643 to simplify the square root of 58643 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 58643 and then take the square root of that product. The prime factors that multiply together to make 58643 are 13 x 13 x 347. 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 58643 by the number (A) squared. 13 squared is 169 and 58643 divided by 169 is 347. Therefore, B equals 347.

Once again we have A and B and can get our answer to 58643 in its simplest radical form as follows:

√58643 = A√B

√58643 = 13√347

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Simplify Square Root of 58644
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