Simplify Square Root of 50396

Here we will show you two methods that you can use to simplify the square root of 50396. In other words, we will show you how to find the square root of 50396 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.

√50396 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50396 to simplify the square root of 50396. 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 50396. The factors of 50396 are 1, 2, 4, 43, 86, 172, 293, 586, 1172, 12599, 25198, and 50396. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 50396 divided by the greatest perfect square from the list of all factors of 50396. We determined above that the greatest perfect square from the list of all factors of 50396 is 4. Furthermore, 50396 divided by 4 is 12599, therefore B equals 12599.

Now we have A and B and can get our answer to 50396 in its simplest radical form as follows:

√50396 = A√B

√50396 = 2√12599

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50396 to simplify the square root of 50396 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 50396 and then take the square root of that product. The prime factors that multiply together to make 50396 are 2 x 2 x 43 x 293. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 50396 by the number (A) squared. 2 squared is 4 and 50396 divided by 4 is 12599. Therefore, B equals 12599.

Once again we have A and B and can get our answer to 50396 in its simplest radical form as follows:

√50396 = A√B

√50396 = 2√12599

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Simplify Square Root of 50397
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