Simplify Square Root of 23353

Here we will show you two methods that you can use to simplify the square root of 23353. In other words, we will show you how to find the square root of 23353 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.

√23353 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23353 to simplify the square root of 23353. 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 23353. The factors of 23353 are 1, 11, 121, 193, 2123, and 23353. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 23353 divided by the greatest perfect square from the list of all factors of 23353. We determined above that the greatest perfect square from the list of all factors of 23353 is 121. Furthermore, 23353 divided by 121 is 193, therefore B equals 193.

Now we have A and B and can get our answer to 23353 in its simplest radical form as follows:

√23353 = A√B

√23353 = 11√193

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23353 to simplify the square root of 23353 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 23353 and then take the square root of that product. The prime factors that multiply together to make 23353 are 11 x 11 x 193. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 23353 by the number (A) squared. 11 squared is 121 and 23353 divided by 121 is 193. Therefore, B equals 193.

Once again we have A and B and can get our answer to 23353 in its simplest radical form as follows:

√23353 = A√B

√23353 = 11√193

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Simplify Square Root of 23354
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