Simplify Square Root of 18348

Here we will show you two methods that you can use to simplify the square root of 18348. In other words, we will show you how to find the square root of 18348 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.

√18348 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18348 to simplify the square root of 18348. 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 18348. The factors of 18348 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 139, 278, 417, 556, 834, 1529, 1668, 3058, 4587, 6116, 9174, and 18348. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 18348 divided by the greatest perfect square from the list of all factors of 18348. We determined above that the greatest perfect square from the list of all factors of 18348 is 4. Furthermore, 18348 divided by 4 is 4587, therefore B equals 4587.

Now we have A and B and can get our answer to 18348 in its simplest radical form as follows:

√18348 = A√B

√18348 = 2√4587

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18348 to simplify the square root of 18348 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 18348 and then take the square root of that product. The prime factors that multiply together to make 18348 are 2 x 2 x 3 x 11 x 139. 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 18348 by the number (A) squared. 2 squared is 4 and 18348 divided by 4 is 4587. Therefore, B equals 4587.

Once again we have A and B and can get our answer to 18348 in its simplest radical form as follows:

√18348 = A√B

√18348 = 2√4587

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Simplify Square Root of 18349
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