Simplify Square Root of 49184

Here we will show you two methods that you can use to simplify the square root of 49184. In other words, we will show you how to find the square root of 49184 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.

√49184 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49184 to simplify the square root of 49184. 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 49184. The factors of 49184 are 1, 2, 4, 8, 16, 29, 32, 53, 58, 106, 116, 212, 232, 424, 464, 848, 928, 1537, 1696, 3074, 6148, 12296, 24592, and 49184. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 49184 divided by the greatest perfect square from the list of all factors of 49184. We determined above that the greatest perfect square from the list of all factors of 49184 is 16. Furthermore, 49184 divided by 16 is 3074, therefore B equals 3074.

Now we have A and B and can get our answer to 49184 in its simplest radical form as follows:

√49184 = A√B

√49184 = 4√3074

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49184 to simplify the square root of 49184 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 49184 and then take the square root of that product. The prime factors that multiply together to make 49184 are 2 x 2 x 2 x 2 x 2 x 29 x 53. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 49184 by the number (A) squared. 4 squared is 16 and 49184 divided by 16 is 3074. Therefore, B equals 3074.

Once again we have A and B and can get our answer to 49184 in its simplest radical form as follows:

√49184 = A√B

√49184 = 4√3074

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