Simplify Square Root of 49088

Here we will show you two methods that you can use to simplify the square root of 49088. In other words, we will show you how to find the square root of 49088 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.

√49088 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49088 to simplify the square root of 49088. 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 49088. The factors of 49088 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 59, 64, 104, 118, 208, 236, 416, 472, 767, 832, 944, 1534, 1888, 3068, 3776, 6136, 12272, 24544, and 49088. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 49088 divided by the greatest perfect square from the list of all factors of 49088. We determined above that the greatest perfect square from the list of all factors of 49088 is 64. Furthermore, 49088 divided by 64 is 767, therefore B equals 767.

Now we have A and B and can get our answer to 49088 in its simplest radical form as follows:

√49088 = A√B

√49088 = 8√767

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49088 to simplify the square root of 49088 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 49088 and then take the square root of that product. The prime factors that multiply together to make 49088 are 2 x 2 x 2 x 2 x 2 x 2 x 13 x 59. 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 49088 by the number (A) squared. 8 squared is 64 and 49088 divided by 64 is 767. Therefore, B equals 767.

Once again we have A and B and can get our answer to 49088 in its simplest radical form as follows:

√49088 = A√B

√49088 = 8√767

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Simplify Square Root of 49089
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