Simplify Square Root of 78416

Here we will show you two methods that you can use to simplify the square root of 78416. In other words, we will show you how to find the square root of 78416 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.

√78416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78416 to simplify the square root of 78416. 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 78416. The factors of 78416 are 1, 2, 4, 8, 13, 16, 26, 29, 52, 58, 104, 116, 169, 208, 232, 338, 377, 464, 676, 754, 1352, 1508, 2704, 3016, 4901, 6032, 9802, 19604, 39208, and 78416. Furthermore, the greatest perfect square on this list is 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Calculate 78416 divided by the greatest perfect square from the list of all factors of 78416. We determined above that the greatest perfect square from the list of all factors of 78416 is 2704. Furthermore, 78416 divided by 2704 is 29, therefore B equals 29.

Now we have A and B and can get our answer to 78416 in its simplest radical form as follows:

√78416 = A√B

√78416 = 52√29

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78416 to simplify the square root of 78416 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 78416 and then take the square root of that product. The prime factors that multiply together to make 78416 are 2 x 2 x 2 x 2 x 13 x 13 x 29. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 13 x 13 = 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Divide 78416 by the number (A) squared. 52 squared is 2704 and 78416 divided by 2704 is 29. Therefore, B equals 29.

Once again we have A and B and can get our answer to 78416 in its simplest radical form as follows:

√78416 = A√B

√78416 = 52√29

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