Simplify Square Root of 20000

Here we will show you two methods that you can use to simplify the square root of 20000. In other words, we will show you how to find the square root of 20000 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.

√20000 = A√B

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

B = Calculate 20000 divided by the greatest perfect square from the list of all factors of 20000. We determined above that the greatest perfect square from the list of all factors of 20000 is 10000. Furthermore, 20000 divided by 10000 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 20000 in its simplest radical form as follows:

√20000 = A√B

√20000 = 100√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20000 to simplify the square root of 20000 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 20000 and then take the square root of that product. The prime factors that multiply together to make 20000 are 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 5 x 5 x 5 x 5 = 10000 and the square root of 10000 is 100. Therefore, A equals 100.

B = Divide 20000 by the number (A) squared. 100 squared is 10000 and 20000 divided by 10000 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 20000 in its simplest radical form as follows:

√20000 = A√B

√20000 = 100√2

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Simplify Square Root of 20001
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