Simplify Square Root of 84966

Here we will show you two methods that you can use to simplify the square root of 84966. In other words, we will show you how to find the square root of 84966 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.

√84966 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84966 to simplify the square root of 84966. 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 84966. The factors of 84966 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 49, 51, 98, 102, 119, 147, 238, 289, 294, 357, 578, 714, 833, 867, 1666, 1734, 2023, 2499, 4046, 4998, 6069, 12138, 14161, 28322, 42483, and 84966. Furthermore, the greatest perfect square on this list is 14161 and the square root of 14161 is 119. Therefore, A equals 119.

B = Calculate 84966 divided by the greatest perfect square from the list of all factors of 84966. We determined above that the greatest perfect square from the list of all factors of 84966 is 14161. Furthermore, 84966 divided by 14161 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 84966 in its simplest radical form as follows:

√84966 = A√B

√84966 = 119√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84966 to simplify the square root of 84966 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 84966 and then take the square root of that product. The prime factors that multiply together to make 84966 are 2 x 3 x 7 x 7 x 17 x 17. When we strip out the pairs only, we get 7 x 7 x 17 x 17 = 14161 and the square root of 14161 is 119. Therefore, A equals 119.

B = Divide 84966 by the number (A) squared. 119 squared is 14161 and 84966 divided by 14161 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 84966 in its simplest radical form as follows:

√84966 = A√B

√84966 = 119√6

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