Simplify Square Root of 49056

Here we will show you two methods that you can use to simplify the square root of 49056. In other words, we will show you how to find the square root of 49056 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.

√49056 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49056 to simplify the square root of 49056. 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 49056. The factors of 49056 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 73, 84, 96, 112, 146, 168, 219, 224, 292, 336, 438, 511, 584, 672, 876, 1022, 1168, 1533, 1752, 2044, 2336, 3066, 3504, 4088, 6132, 7008, 8176, 12264, 16352, 24528, and 49056. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 49056 divided by the greatest perfect square from the list of all factors of 49056. We determined above that the greatest perfect square from the list of all factors of 49056 is 16. Furthermore, 49056 divided by 16 is 3066, therefore B equals 3066.

Now we have A and B and can get our answer to 49056 in its simplest radical form as follows:

√49056 = A√B

√49056 = 4√3066

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49056 to simplify the square root of 49056 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 49056 and then take the square root of that product. The prime factors that multiply together to make 49056 are 2 x 2 x 2 x 2 x 2 x 3 x 7 x 73. 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 49056 by the number (A) squared. 4 squared is 16 and 49056 divided by 16 is 3066. Therefore, B equals 3066.

Once again we have A and B and can get our answer to 49056 in its simplest radical form as follows:

√49056 = A√B

√49056 = 4√3066

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