Simplify Square Root of 80190

Here we will show you two methods that you can use to simplify the square root of 80190. In other words, we will show you how to find the square root of 80190 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.

√80190 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80190 to simplify the square root of 80190. 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 80190. The factors of 80190 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 81, 90, 99, 110, 135, 162, 165, 198, 243, 270, 297, 330, 405, 486, 495, 594, 729, 810, 891, 990, 1215, 1458, 1485, 1782, 2430, 2673, 2970, 3645, 4455, 5346, 7290, 8019, 8910, 13365, 16038, 26730, 40095, and 80190. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 80190 divided by the greatest perfect square from the list of all factors of 80190. We determined above that the greatest perfect square from the list of all factors of 80190 is 729. Furthermore, 80190 divided by 729 is 110, therefore B equals 110.

Now we have A and B and can get our answer to 80190 in its simplest radical form as follows:

√80190 = A√B

√80190 = 27√110

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80190 to simplify the square root of 80190 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 80190 and then take the square root of that product. The prime factors that multiply together to make 80190 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5 x 11. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 80190 by the number (A) squared. 27 squared is 729 and 80190 divided by 729 is 110. Therefore, B equals 110.

Once again we have A and B and can get our answer to 80190 in its simplest radical form as follows:

√80190 = A√B

√80190 = 27√110

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Simplify Square Root of 80191
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