Simplify Square Root of 36522

Here we will show you two methods that you can use to simplify the square root of 36522. In other words, we will show you how to find the square root of 36522 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.

√36522 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36522 to simplify the square root of 36522. 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 36522. The factors of 36522 are 1, 2, 3, 6, 9, 18, 2029, 4058, 6087, 12174, 18261, and 36522. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 36522 divided by the greatest perfect square from the list of all factors of 36522. We determined above that the greatest perfect square from the list of all factors of 36522 is 9. Furthermore, 36522 divided by 9 is 4058, therefore B equals 4058.

Now we have A and B and can get our answer to 36522 in its simplest radical form as follows:

√36522 = A√B

√36522 = 3√4058

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36522 to simplify the square root of 36522 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 36522 and then take the square root of that product. The prime factors that multiply together to make 36522 are 2 x 3 x 3 x 2029. 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 36522 by the number (A) squared. 3 squared is 9 and 36522 divided by 9 is 4058. Therefore, B equals 4058.

Once again we have A and B and can get our answer to 36522 in its simplest radical form as follows:

√36522 = A√B

√36522 = 3√4058

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Simplify Square Root of 36523
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