Simplify Square Root of 92950

Here we will show you two methods that you can use to simplify the square root of 92950. In other words, we will show you how to find the square root of 92950 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.

√92950 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92950 to simplify the square root of 92950. 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 92950. The factors of 92950 are 1, 2, 5, 10, 11, 13, 22, 25, 26, 50, 55, 65, 110, 130, 143, 169, 275, 286, 325, 338, 550, 650, 715, 845, 1430, 1690, 1859, 3575, 3718, 4225, 7150, 8450, 9295, 18590, 46475, and 92950. Furthermore, the greatest perfect square on this list is 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Calculate 92950 divided by the greatest perfect square from the list of all factors of 92950. We determined above that the greatest perfect square from the list of all factors of 92950 is 4225. Furthermore, 92950 divided by 4225 is 22, therefore B equals 22.

Now we have A and B and can get our answer to 92950 in its simplest radical form as follows:

√92950 = A√B

√92950 = 65√22

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92950 to simplify the square root of 92950 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 92950 and then take the square root of that product. The prime factors that multiply together to make 92950 are 2 x 5 x 5 x 11 x 13 x 13. When we strip out the pairs only, we get 5 x 5 x 13 x 13 = 4225 and the square root of 4225 is 65. Therefore, A equals 65.

B = Divide 92950 by the number (A) squared. 65 squared is 4225 and 92950 divided by 4225 is 22. Therefore, B equals 22.

Once again we have A and B and can get our answer to 92950 in its simplest radical form as follows:

√92950 = A√B

√92950 = 65√22

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Simplify Square Root of 92951
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