Simplify Square Root of 95175

Here we will show you two methods that you can use to simplify the square root of 95175. In other words, we will show you how to find the square root of 95175 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.

√95175 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95175 to simplify the square root of 95175. 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 95175. The factors of 95175 are 1, 3, 5, 9, 15, 25, 27, 45, 47, 75, 81, 135, 141, 225, 235, 405, 423, 675, 705, 1175, 1269, 2025, 2115, 3525, 3807, 6345, 10575, 19035, 31725, and 95175. Furthermore, the greatest perfect square on this list is 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Calculate 95175 divided by the greatest perfect square from the list of all factors of 95175. We determined above that the greatest perfect square from the list of all factors of 95175 is 2025. Furthermore, 95175 divided by 2025 is 47, therefore B equals 47.

Now we have A and B and can get our answer to 95175 in its simplest radical form as follows:

√95175 = A√B

√95175 = 45√47

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95175 to simplify the square root of 95175 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 95175 and then take the square root of that product. The prime factors that multiply together to make 95175 are 3 x 3 x 3 x 3 x 5 x 5 x 47. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 5 x 5 = 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Divide 95175 by the number (A) squared. 45 squared is 2025 and 95175 divided by 2025 is 47. Therefore, B equals 47.

Once again we have A and B and can get our answer to 95175 in its simplest radical form as follows:

√95175 = A√B

√95175 = 45√47

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