Simplify Square Root of 4698

Here we will show you two methods that you can use to simplify the square root of 4698. In other words, we will show you how to find the square root of 4698 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.

√4698 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4698 to simplify the square root of 4698. 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 4698. The factors of 4698 are 1, 2, 3, 6, 9, 18, 27, 29, 54, 58, 81, 87, 162, 174, 261, 522, 783, 1566, 2349, and 4698. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 4698 divided by the greatest perfect square from the list of all factors of 4698. We determined above that the greatest perfect square from the list of all factors of 4698 is 81. Furthermore, 4698 divided by 81 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 4698 in its simplest radical form as follows:

√4698 = A√B

√4698 = 9√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4698 to simplify the square root of 4698 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 4698 and then take the square root of that product. The prime factors that multiply together to make 4698 are 2 x 3 x 3 x 3 x 3 x 29. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 4698 by the number (A) squared. 9 squared is 81 and 4698 divided by 81 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 4698 in its simplest radical form as follows:

√4698 = A√B

√4698 = 9√58

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Simplify Square Root of 4699
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