Simplify Square Root of 66139

Here we will show you two methods that you can use to simplify the square root of 66139. In other words, we will show you how to find the square root of 66139 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.

√66139 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66139 to simplify the square root of 66139. 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 66139. The factors of 66139 are 1, 19, 59, 1121, 3481, and 66139. Furthermore, the greatest perfect square on this list is 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Calculate 66139 divided by the greatest perfect square from the list of all factors of 66139. We determined above that the greatest perfect square from the list of all factors of 66139 is 3481. Furthermore, 66139 divided by 3481 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 66139 in its simplest radical form as follows:

√66139 = A√B

√66139 = 59√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66139 to simplify the square root of 66139 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 66139 and then take the square root of that product. The prime factors that multiply together to make 66139 are 19 x 59 x 59. When we strip out the pairs only, we get 59 x 59 = 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Divide 66139 by the number (A) squared. 59 squared is 3481 and 66139 divided by 3481 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 66139 in its simplest radical form as follows:

√66139 = A√B

√66139 = 59√19

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Simplify Square Root of 66140
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