Simplify Square Root of 65522

Here we will show you two methods that you can use to simplify the square root of 65522. In other words, we will show you how to find the square root of 65522 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.

√65522 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65522 to simplify the square root of 65522. 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 65522. The factors of 65522 are 1, 2, 181, 362, 32761, and 65522. Furthermore, the greatest perfect square on this list is 32761 and the square root of 32761 is 181. Therefore, A equals 181.

B = Calculate 65522 divided by the greatest perfect square from the list of all factors of 65522. We determined above that the greatest perfect square from the list of all factors of 65522 is 32761. Furthermore, 65522 divided by 32761 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 65522 in its simplest radical form as follows:

√65522 = A√B

√65522 = 181√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65522 to simplify the square root of 65522 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 65522 and then take the square root of that product. The prime factors that multiply together to make 65522 are 2 x 181 x 181. When we strip out the pairs only, we get 181 x 181 = 32761 and the square root of 32761 is 181. Therefore, A equals 181.

B = Divide 65522 by the number (A) squared. 181 squared is 32761 and 65522 divided by 32761 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 65522 in its simplest radical form as follows:

√65522 = A√B

√65522 = 181√2

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Simplify Square Root of 65523
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