Simplify Square Root of 77872

Here we will show you two methods that you can use to simplify the square root of 77872. In other words, we will show you how to find the square root of 77872 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.

√77872 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77872 to simplify the square root of 77872. 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 77872. The factors of 77872 are 1, 2, 4, 8, 16, 31, 62, 124, 157, 248, 314, 496, 628, 1256, 2512, 4867, 9734, 19468, 38936, and 77872. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 77872 divided by the greatest perfect square from the list of all factors of 77872. We determined above that the greatest perfect square from the list of all factors of 77872 is 16. Furthermore, 77872 divided by 16 is 4867, therefore B equals 4867.

Now we have A and B and can get our answer to 77872 in its simplest radical form as follows:

√77872 = A√B

√77872 = 4√4867

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77872 to simplify the square root of 77872 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 77872 and then take the square root of that product. The prime factors that multiply together to make 77872 are 2 x 2 x 2 x 2 x 31 x 157. 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 77872 by the number (A) squared. 4 squared is 16 and 77872 divided by 16 is 4867. Therefore, B equals 4867.

Once again we have A and B and can get our answer to 77872 in its simplest radical form as follows:

√77872 = A√B

√77872 = 4√4867

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Simplify Square Root of 77873
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