Simplify Square Root of 52182

Here we will show you two methods that you can use to simplify the square root of 52182. In other words, we will show you how to find the square root of 52182 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.

√52182 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52182 to simplify the square root of 52182. 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 52182. The factors of 52182 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 223, 234, 446, 669, 1338, 2007, 2899, 4014, 5798, 8697, 17394, 26091, and 52182. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 52182 divided by the greatest perfect square from the list of all factors of 52182. We determined above that the greatest perfect square from the list of all factors of 52182 is 9. Furthermore, 52182 divided by 9 is 5798, therefore B equals 5798.

Now we have A and B and can get our answer to 52182 in its simplest radical form as follows:

√52182 = A√B

√52182 = 3√5798

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52182 to simplify the square root of 52182 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 52182 and then take the square root of that product. The prime factors that multiply together to make 52182 are 2 x 3 x 3 x 13 x 223. 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 52182 by the number (A) squared. 3 squared is 9 and 52182 divided by 9 is 5798. Therefore, B equals 5798.

Once again we have A and B and can get our answer to 52182 in its simplest radical form as follows:

√52182 = A√B

√52182 = 3√5798

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Simplify Square Root of 52183
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