Simplify Square Root of 80262

Here we will show you two methods that you can use to simplify the square root of 80262. In other words, we will show you how to find the square root of 80262 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.

√80262 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80262 to simplify the square root of 80262. 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 80262. The factors of 80262 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 49, 63, 78, 91, 98, 117, 126, 147, 182, 234, 273, 294, 343, 441, 546, 637, 686, 819, 882, 1029, 1274, 1638, 1911, 2058, 3087, 3822, 4459, 5733, 6174, 8918, 11466, 13377, 26754, 40131, and 80262. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 80262 divided by the greatest perfect square from the list of all factors of 80262. We determined above that the greatest perfect square from the list of all factors of 80262 is 441. Furthermore, 80262 divided by 441 is 182, therefore B equals 182.

Now we have A and B and can get our answer to 80262 in its simplest radical form as follows:

√80262 = A√B

√80262 = 21√182

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80262 to simplify the square root of 80262 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 80262 and then take the square root of that product. The prime factors that multiply together to make 80262 are 2 x 3 x 3 x 7 x 7 x 7 x 13. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 80262 by the number (A) squared. 21 squared is 441 and 80262 divided by 441 is 182. Therefore, B equals 182.

Once again we have A and B and can get our answer to 80262 in its simplest radical form as follows:

√80262 = A√B

√80262 = 21√182

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Simplify Square Root of 80263
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