Simplify Square Root of 80000

Here we will show you two methods that you can use to simplify the square root of 80000. In other words, we will show you how to find the square root of 80000 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.

√80000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80000 to simplify the square root of 80000. 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 80000. The factors of 80000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 320, 400, 500, 625, 640, 800, 1000, 1250, 1600, 2000, 2500, 3200, 4000, 5000, 8000, 10000, 16000, 20000, 40000, and 80000. Furthermore, the greatest perfect square on this list is 40000 and the square root of 40000 is 200. Therefore, A equals 200.

B = Calculate 80000 divided by the greatest perfect square from the list of all factors of 80000. We determined above that the greatest perfect square from the list of all factors of 80000 is 40000. Furthermore, 80000 divided by 40000 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 80000 in its simplest radical form as follows:

√80000 = A√B

√80000 = 200√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80000 to simplify the square root of 80000 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 80000 and then take the square root of that product. The prime factors that multiply together to make 80000 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 = 40000 and the square root of 40000 is 200. Therefore, A equals 200.

B = Divide 80000 by the number (A) squared. 200 squared is 40000 and 80000 divided by 40000 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 80000 in its simplest radical form as follows:

√80000 = A√B

√80000 = 200√2

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Simplify Square Root of 80001
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