Simplify Square Root of 59643

Here we will show you two methods that you can use to simplify the square root of 59643. In other words, we will show you how to find the square root of 59643 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.

√59643 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59643 to simplify the square root of 59643. 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 59643. The factors of 59643 are 1, 3, 9, 27, 47, 141, 423, 1269, 2209, 6627, 19881, and 59643. Furthermore, the greatest perfect square on this list is 19881 and the square root of 19881 is 141. Therefore, A equals 141.

B = Calculate 59643 divided by the greatest perfect square from the list of all factors of 59643. We determined above that the greatest perfect square from the list of all factors of 59643 is 19881. Furthermore, 59643 divided by 19881 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 59643 in its simplest radical form as follows:

√59643 = A√B

√59643 = 141√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59643 to simplify the square root of 59643 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 59643 and then take the square root of that product. The prime factors that multiply together to make 59643 are 3 x 3 x 3 x 47 x 47. When we strip out the pairs only, we get 3 x 3 x 47 x 47 = 19881 and the square root of 19881 is 141. Therefore, A equals 141.

B = Divide 59643 by the number (A) squared. 141 squared is 19881 and 59643 divided by 19881 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 59643 in its simplest radical form as follows:

√59643 = A√B

√59643 = 141√3

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Simplify Square Root of 59644
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