Simplify Square Root of 49216

Here we will show you two methods that you can use to simplify the square root of 49216. In other words, we will show you how to find the square root of 49216 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.

√49216 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49216 to simplify the square root of 49216. 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 49216. The factors of 49216 are 1, 2, 4, 8, 16, 32, 64, 769, 1538, 3076, 6152, 12304, 24608, and 49216. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 49216 divided by the greatest perfect square from the list of all factors of 49216. We determined above that the greatest perfect square from the list of all factors of 49216 is 64. Furthermore, 49216 divided by 64 is 769, therefore B equals 769.

Now we have A and B and can get our answer to 49216 in its simplest radical form as follows:

√49216 = A√B

√49216 = 8√769

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49216 to simplify the square root of 49216 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 49216 and then take the square root of that product. The prime factors that multiply together to make 49216 are 2 x 2 x 2 x 2 x 2 x 2 x 769. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 49216 by the number (A) squared. 8 squared is 64 and 49216 divided by 64 is 769. Therefore, B equals 769.

Once again we have A and B and can get our answer to 49216 in its simplest radical form as follows:

√49216 = A√B

√49216 = 8√769

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Simplify Square Root of 49217
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