Simplify Square Root of 45198

Here we will show you two methods that you can use to simplify the square root of 45198. In other words, we will show you how to find the square root of 45198 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.

√45198 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45198 to simplify the square root of 45198. 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 45198. The factors of 45198 are 1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 81, 93, 162, 186, 243, 279, 486, 558, 729, 837, 1458, 1674, 2511, 5022, 7533, 15066, 22599, and 45198. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 45198 divided by the greatest perfect square from the list of all factors of 45198. We determined above that the greatest perfect square from the list of all factors of 45198 is 729. Furthermore, 45198 divided by 729 is 62, therefore B equals 62.

Now we have A and B and can get our answer to 45198 in its simplest radical form as follows:

√45198 = A√B

√45198 = 27√62

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45198 to simplify the square root of 45198 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 45198 and then take the square root of that product. The prime factors that multiply together to make 45198 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 31. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 45198 by the number (A) squared. 27 squared is 729 and 45198 divided by 729 is 62. Therefore, B equals 62.

Once again we have A and B and can get our answer to 45198 in its simplest radical form as follows:

√45198 = A√B

√45198 = 27√62

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