Simplify Square Root of 80465

Here we will show you two methods that you can use to simplify the square root of 80465. In other words, we will show you how to find the square root of 80465 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.

√80465 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80465 to simplify the square root of 80465. 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 80465. The factors of 80465 are 1, 5, 7, 11, 19, 35, 55, 77, 95, 121, 133, 209, 385, 605, 665, 847, 1045, 1463, 2299, 4235, 7315, 11495, 16093, and 80465. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 80465 divided by the greatest perfect square from the list of all factors of 80465. We determined above that the greatest perfect square from the list of all factors of 80465 is 121. Furthermore, 80465 divided by 121 is 665, therefore B equals 665.

Now we have A and B and can get our answer to 80465 in its simplest radical form as follows:

√80465 = A√B

√80465 = 11√665

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80465 to simplify the square root of 80465 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 80465 and then take the square root of that product. The prime factors that multiply together to make 80465 are 5 x 7 x 11 x 11 x 19. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 80465 by the number (A) squared. 11 squared is 121 and 80465 divided by 121 is 665. Therefore, B equals 665.

Once again we have A and B and can get our answer to 80465 in its simplest radical form as follows:

√80465 = A√B

√80465 = 11√665

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Simplify Square Root of 80466
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