Simplify Square Root of 50869

Here we will show you two methods that you can use to simplify the square root of 50869. In other words, we will show you how to find the square root of 50869 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.

√50869 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50869 to simplify the square root of 50869. 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 50869. The factors of 50869 are 1, 7, 13, 43, 91, 169, 301, 559, 1183, 3913, 7267, and 50869. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 50869 divided by the greatest perfect square from the list of all factors of 50869. We determined above that the greatest perfect square from the list of all factors of 50869 is 169. Furthermore, 50869 divided by 169 is 301, therefore B equals 301.

Now we have A and B and can get our answer to 50869 in its simplest radical form as follows:

√50869 = A√B

√50869 = 13√301

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50869 to simplify the square root of 50869 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 50869 and then take the square root of that product. The prime factors that multiply together to make 50869 are 7 x 13 x 13 x 43. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 50869 by the number (A) squared. 13 squared is 169 and 50869 divided by 169 is 301. Therefore, B equals 301.

Once again we have A and B and can get our answer to 50869 in its simplest radical form as follows:

√50869 = A√B

√50869 = 13√301

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Simplify Square Root of 50870
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