Simplify Square Root of 95052

Here we will show you two methods that you can use to simplify the square root of 95052. In other words, we will show you how to find the square root of 95052 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.

√95052 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95052 to simplify the square root of 95052. 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 95052. The factors of 95052 are 1, 2, 3, 4, 6, 12, 89, 178, 267, 356, 534, 1068, 7921, 15842, 23763, 31684, 47526, and 95052. Furthermore, the greatest perfect square on this list is 31684 and the square root of 31684 is 178. Therefore, A equals 178.

B = Calculate 95052 divided by the greatest perfect square from the list of all factors of 95052. We determined above that the greatest perfect square from the list of all factors of 95052 is 31684. Furthermore, 95052 divided by 31684 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 95052 in its simplest radical form as follows:

√95052 = A√B

√95052 = 178√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95052 to simplify the square root of 95052 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 95052 and then take the square root of that product. The prime factors that multiply together to make 95052 are 2 x 2 x 3 x 89 x 89. When we strip out the pairs only, we get 2 x 2 x 89 x 89 = 31684 and the square root of 31684 is 178. Therefore, A equals 178.

B = Divide 95052 by the number (A) squared. 178 squared is 31684 and 95052 divided by 31684 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 95052 in its simplest radical form as follows:

√95052 = A√B

√95052 = 178√3

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Simplify Square Root of 95053
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