Simplify Square Root of 94178

Here we will show you two methods that you can use to simplify the square root of 94178. In other words, we will show you how to find the square root of 94178 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.

√94178 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 94178 to simplify the square root of 94178. 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 94178. The factors of 94178 are 1, 2, 7, 14, 31, 49, 62, 98, 217, 434, 961, 1519, 1922, 3038, 6727, 13454, 47089, and 94178. Furthermore, the greatest perfect square on this list is 47089 and the square root of 47089 is 217. Therefore, A equals 217.

B = Calculate 94178 divided by the greatest perfect square from the list of all factors of 94178. We determined above that the greatest perfect square from the list of all factors of 94178 is 47089. Furthermore, 94178 divided by 47089 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 94178 in its simplest radical form as follows:

√94178 = A√B

√94178 = 217√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 94178 to simplify the square root of 94178 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 94178 and then take the square root of that product. The prime factors that multiply together to make 94178 are 2 x 7 x 7 x 31 x 31. When we strip out the pairs only, we get 7 x 7 x 31 x 31 = 47089 and the square root of 47089 is 217. Therefore, A equals 217.

B = Divide 94178 by the number (A) squared. 217 squared is 47089 and 94178 divided by 47089 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 94178 in its simplest radical form as follows:

√94178 = A√B

√94178 = 217√2

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Simplify Square Root of 94179
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