Simplify Square Root of 80360

Here we will show you two methods that you can use to simplify the square root of 80360. In other words, we will show you how to find the square root of 80360 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.

√80360 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80360 to simplify the square root of 80360. 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 80360. The factors of 80360 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 41, 49, 56, 70, 82, 98, 140, 164, 196, 205, 245, 280, 287, 328, 392, 410, 490, 574, 820, 980, 1148, 1435, 1640, 1960, 2009, 2296, 2870, 4018, 5740, 8036, 10045, 11480, 16072, 20090, 40180, and 80360. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 80360 divided by the greatest perfect square from the list of all factors of 80360. We determined above that the greatest perfect square from the list of all factors of 80360 is 196. Furthermore, 80360 divided by 196 is 410, therefore B equals 410.

Now we have A and B and can get our answer to 80360 in its simplest radical form as follows:

√80360 = A√B

√80360 = 14√410

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80360 to simplify the square root of 80360 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 80360 and then take the square root of that product. The prime factors that multiply together to make 80360 are 2 x 2 x 2 x 5 x 7 x 7 x 41. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 80360 by the number (A) squared. 14 squared is 196 and 80360 divided by 196 is 410. Therefore, B equals 410.

Once again we have A and B and can get our answer to 80360 in its simplest radical form as follows:

√80360 = A√B

√80360 = 14√410

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Simplify Square Root of 80361
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