Simplify Square Root of 80444

Here we will show you two methods that you can use to simplify the square root of 80444. In other words, we will show you how to find the square root of 80444 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.

√80444 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80444 to simplify the square root of 80444. 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 80444. The factors of 80444 are 1, 2, 4, 7, 13, 14, 17, 26, 28, 34, 52, 68, 91, 119, 169, 182, 221, 238, 338, 364, 442, 476, 676, 884, 1183, 1547, 2366, 2873, 3094, 4732, 5746, 6188, 11492, 20111, 40222, and 80444. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 80444 divided by the greatest perfect square from the list of all factors of 80444. We determined above that the greatest perfect square from the list of all factors of 80444 is 676. Furthermore, 80444 divided by 676 is 119, therefore B equals 119.

Now we have A and B and can get our answer to 80444 in its simplest radical form as follows:

√80444 = A√B

√80444 = 26√119

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80444 to simplify the square root of 80444 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 80444 and then take the square root of that product. The prime factors that multiply together to make 80444 are 2 x 2 x 7 x 13 x 13 x 17. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 80444 by the number (A) squared. 26 squared is 676 and 80444 divided by 676 is 119. Therefore, B equals 119.

Once again we have A and B and can get our answer to 80444 in its simplest radical form as follows:

√80444 = A√B

√80444 = 26√119

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