Simplify Square Root of 84941

Here we will show you two methods that you can use to simplify the square root of 84941. In other words, we will show you how to find the square root of 84941 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.

√84941 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84941 to simplify the square root of 84941. 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 84941. The factors of 84941 are 1, 29, 101, 841, 2929, and 84941. Furthermore, the greatest perfect square on this list is 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Calculate 84941 divided by the greatest perfect square from the list of all factors of 84941. We determined above that the greatest perfect square from the list of all factors of 84941 is 841. Furthermore, 84941 divided by 841 is 101, therefore B equals 101.

Now we have A and B and can get our answer to 84941 in its simplest radical form as follows:

√84941 = A√B

√84941 = 29√101

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84941 to simplify the square root of 84941 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 84941 and then take the square root of that product. The prime factors that multiply together to make 84941 are 29 x 29 x 101. When we strip out the pairs only, we get 29 x 29 = 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Divide 84941 by the number (A) squared. 29 squared is 841 and 84941 divided by 841 is 101. Therefore, B equals 101.

Once again we have A and B and can get our answer to 84941 in its simplest radical form as follows:

√84941 = A√B

√84941 = 29√101

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Simplify Square Root of 84942
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