Simplify Square Root of 49972

Here we will show you two methods that you can use to simplify the square root of 49972. In other words, we will show you how to find the square root of 49972 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.

√49972 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49972 to simplify the square root of 49972. 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 49972. The factors of 49972 are 1, 2, 4, 13, 26, 31, 52, 62, 124, 403, 806, 961, 1612, 1922, 3844, 12493, 24986, and 49972. Furthermore, the greatest perfect square on this list is 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Calculate 49972 divided by the greatest perfect square from the list of all factors of 49972. We determined above that the greatest perfect square from the list of all factors of 49972 is 3844. Furthermore, 49972 divided by 3844 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 49972 in its simplest radical form as follows:

√49972 = A√B

√49972 = 62√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49972 to simplify the square root of 49972 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 49972 and then take the square root of that product. The prime factors that multiply together to make 49972 are 2 x 2 x 13 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 31 x 31 = 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Divide 49972 by the number (A) squared. 62 squared is 3844 and 49972 divided by 3844 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 49972 in its simplest radical form as follows:

√49972 = A√B

√49972 = 62√13

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Simplify Square Root of 49973
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