Simplify Square Root of 77584

Here we will show you two methods that you can use to simplify the square root of 77584. In other words, we will show you how to find the square root of 77584 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.

√77584 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77584 to simplify the square root of 77584. 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 77584. The factors of 77584 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208, 373, 746, 1492, 2984, 4849, 5968, 9698, 19396, 38792, and 77584. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 77584 divided by the greatest perfect square from the list of all factors of 77584. We determined above that the greatest perfect square from the list of all factors of 77584 is 16. Furthermore, 77584 divided by 16 is 4849, therefore B equals 4849.

Now we have A and B and can get our answer to 77584 in its simplest radical form as follows:

√77584 = A√B

√77584 = 4√4849

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77584 to simplify the square root of 77584 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 77584 and then take the square root of that product. The prime factors that multiply together to make 77584 are 2 x 2 x 2 x 2 x 13 x 373. 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 77584 by the number (A) squared. 4 squared is 16 and 77584 divided by 16 is 4849. Therefore, B equals 4849.

Once again we have A and B and can get our answer to 77584 in its simplest radical form as follows:

√77584 = A√B

√77584 = 4√4849

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