Simplify Square Root of 75272

Here we will show you two methods that you can use to simplify the square root of 75272. In other words, we will show you how to find the square root of 75272 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.

√75272 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75272 to simplify the square root of 75272. 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 75272. The factors of 75272 are 1, 2, 4, 8, 97, 194, 388, 776, 9409, 18818, 37636, and 75272. Furthermore, the greatest perfect square on this list is 37636 and the square root of 37636 is 194. Therefore, A equals 194.

B = Calculate 75272 divided by the greatest perfect square from the list of all factors of 75272. We determined above that the greatest perfect square from the list of all factors of 75272 is 37636. Furthermore, 75272 divided by 37636 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 75272 in its simplest radical form as follows:

√75272 = A√B

√75272 = 194√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75272 to simplify the square root of 75272 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 75272 and then take the square root of that product. The prime factors that multiply together to make 75272 are 2 x 2 x 2 x 97 x 97. When we strip out the pairs only, we get 2 x 2 x 97 x 97 = 37636 and the square root of 37636 is 194. Therefore, A equals 194.

B = Divide 75272 by the number (A) squared. 194 squared is 37636 and 75272 divided by 37636 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 75272 in its simplest radical form as follows:

√75272 = A√B

√75272 = 194√2

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Simplify Square Root of 75273
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