Simplify Square Root of 18292

Here we will show you two methods that you can use to simplify the square root of 18292. In other words, we will show you how to find the square root of 18292 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.

√18292 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18292 to simplify the square root of 18292. 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 18292. The factors of 18292 are 1, 2, 4, 17, 34, 68, 269, 538, 1076, 4573, 9146, and 18292. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 18292 divided by the greatest perfect square from the list of all factors of 18292. We determined above that the greatest perfect square from the list of all factors of 18292 is 4. Furthermore, 18292 divided by 4 is 4573, therefore B equals 4573.

Now we have A and B and can get our answer to 18292 in its simplest radical form as follows:

√18292 = A√B

√18292 = 2√4573

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18292 to simplify the square root of 18292 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 18292 and then take the square root of that product. The prime factors that multiply together to make 18292 are 2 x 2 x 17 x 269. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 18292 by the number (A) squared. 2 squared is 4 and 18292 divided by 4 is 4573. Therefore, B equals 4573.

Once again we have A and B and can get our answer to 18292 in its simplest radical form as follows:

√18292 = A√B

√18292 = 2√4573

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Simplify Square Root of 18293
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