Simplify Square Root of 55314

Here we will show you two methods that you can use to simplify the square root of 55314. In other words, we will show you how to find the square root of 55314 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.

√55314 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55314 to simplify the square root of 55314. 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 55314. The factors of 55314 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 439, 878, 1317, 2634, 3073, 3951, 6146, 7902, 9219, 18438, 27657, and 55314. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 55314 divided by the greatest perfect square from the list of all factors of 55314. We determined above that the greatest perfect square from the list of all factors of 55314 is 9. Furthermore, 55314 divided by 9 is 6146, therefore B equals 6146.

Now we have A and B and can get our answer to 55314 in its simplest radical form as follows:

√55314 = A√B

√55314 = 3√6146

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55314 to simplify the square root of 55314 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 55314 and then take the square root of that product. The prime factors that multiply together to make 55314 are 2 x 3 x 3 x 7 x 439. 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 55314 by the number (A) squared. 3 squared is 9 and 55314 divided by 9 is 6146. Therefore, B equals 6146.

Once again we have A and B and can get our answer to 55314 in its simplest radical form as follows:

√55314 = A√B

√55314 = 3√6146

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Simplify Square Root of 55315
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