Simplify Square Root of 80802

Here we will show you two methods that you can use to simplify the square root of 80802. In other words, we will show you how to find the square root of 80802 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.

√80802 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80802 to simplify the square root of 80802. 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 80802. The factors of 80802 are 1, 2, 3, 6, 9, 18, 67, 134, 201, 402, 603, 1206, 4489, 8978, 13467, 26934, 40401, and 80802. Furthermore, the greatest perfect square on this list is 40401 and the square root of 40401 is 201. Therefore, A equals 201.

B = Calculate 80802 divided by the greatest perfect square from the list of all factors of 80802. We determined above that the greatest perfect square from the list of all factors of 80802 is 40401. Furthermore, 80802 divided by 40401 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 80802 in its simplest radical form as follows:

√80802 = A√B

√80802 = 201√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80802 to simplify the square root of 80802 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 80802 and then take the square root of that product. The prime factors that multiply together to make 80802 are 2 x 3 x 3 x 67 x 67. When we strip out the pairs only, we get 3 x 3 x 67 x 67 = 40401 and the square root of 40401 is 201. Therefore, A equals 201.

B = Divide 80802 by the number (A) squared. 201 squared is 40401 and 80802 divided by 40401 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 80802 in its simplest radical form as follows:

√80802 = A√B

√80802 = 201√2

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Simplify Square Root of 80803
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