Simplify Square Root of 19323

Here we will show you two methods that you can use to simplify the square root of 19323. In other words, we will show you how to find the square root of 19323 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.

√19323 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19323 to simplify the square root of 19323. 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 19323. The factors of 19323 are 1, 3, 9, 19, 57, 113, 171, 339, 1017, 2147, 6441, and 19323. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 19323 divided by the greatest perfect square from the list of all factors of 19323. We determined above that the greatest perfect square from the list of all factors of 19323 is 9. Furthermore, 19323 divided by 9 is 2147, therefore B equals 2147.

Now we have A and B and can get our answer to 19323 in its simplest radical form as follows:

√19323 = A√B

√19323 = 3√2147

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19323 to simplify the square root of 19323 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 19323 and then take the square root of that product. The prime factors that multiply together to make 19323 are 3 x 3 x 19 x 113. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 19323 by the number (A) squared. 3 squared is 9 and 19323 divided by 9 is 2147. Therefore, B equals 2147.

Once again we have A and B and can get our answer to 19323 in its simplest radical form as follows:

√19323 = A√B

√19323 = 3√2147

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Simplify Square Root of 19324
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