Simplify Square Root of 19925

Here we will show you two methods that you can use to simplify the square root of 19925. In other words, we will show you how to find the square root of 19925 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.

√19925 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19925 to simplify the square root of 19925. 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 19925. The factors of 19925 are 1, 5, 25, 797, 3985, and 19925. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 19925 divided by the greatest perfect square from the list of all factors of 19925. We determined above that the greatest perfect square from the list of all factors of 19925 is 25. Furthermore, 19925 divided by 25 is 797, therefore B equals 797.

Now we have A and B and can get our answer to 19925 in its simplest radical form as follows:

√19925 = A√B

√19925 = 5√797

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19925 to simplify the square root of 19925 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 19925 and then take the square root of that product. The prime factors that multiply together to make 19925 are 5 x 5 x 797. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 19925 by the number (A) squared. 5 squared is 25 and 19925 divided by 25 is 797. Therefore, B equals 797.

Once again we have A and B and can get our answer to 19925 in its simplest radical form as follows:

√19925 = A√B

√19925 = 5√797

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Simplify Square Root of 19926
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