Simplify Square Root of 76452

Here we will show you two methods that you can use to simplify the square root of 76452. In other words, we will show you how to find the square root of 76452 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.

√76452 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76452 to simplify the square root of 76452. 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 76452. The factors of 76452 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276, 277, 554, 831, 1108, 1662, 3324, 6371, 12742, 19113, 25484, 38226, and 76452. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 76452 divided by the greatest perfect square from the list of all factors of 76452. We determined above that the greatest perfect square from the list of all factors of 76452 is 4. Furthermore, 76452 divided by 4 is 19113, therefore B equals 19113.

Now we have A and B and can get our answer to 76452 in its simplest radical form as follows:

√76452 = A√B

√76452 = 2√19113

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76452 to simplify the square root of 76452 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 76452 and then take the square root of that product. The prime factors that multiply together to make 76452 are 2 x 2 x 3 x 23 x 277. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 76452 by the number (A) squared. 2 squared is 4 and 76452 divided by 4 is 19113. Therefore, B equals 19113.

Once again we have A and B and can get our answer to 76452 in its simplest radical form as follows:

√76452 = A√B

√76452 = 2√19113

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