Simplify Square Root of 91890

Here we will show you two methods that you can use to simplify the square root of 91890. In other words, we will show you how to find the square root of 91890 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.

√91890 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91890 to simplify the square root of 91890. 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 91890. The factors of 91890 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 1021, 2042, 3063, 5105, 6126, 9189, 10210, 15315, 18378, 30630, 45945, and 91890. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 91890 divided by the greatest perfect square from the list of all factors of 91890. We determined above that the greatest perfect square from the list of all factors of 91890 is 9. Furthermore, 91890 divided by 9 is 10210, therefore B equals 10210.

Now we have A and B and can get our answer to 91890 in its simplest radical form as follows:

√91890 = A√B

√91890 = 3√10210

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91890 to simplify the square root of 91890 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 91890 and then take the square root of that product. The prime factors that multiply together to make 91890 are 2 x 3 x 3 x 5 x 1021. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 91890 by the number (A) squared. 3 squared is 9 and 91890 divided by 9 is 10210. Therefore, B equals 10210.

Once again we have A and B and can get our answer to 91890 in its simplest radical form as follows:

√91890 = A√B

√91890 = 3√10210

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