Simplify Square Root of 75809

Here we will show you two methods that you can use to simplify the square root of 75809. In other words, we will show you how to find the square root of 75809 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.

√75809 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75809 to simplify the square root of 75809. 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 75809. The factors of 75809 are 1, 41, 43, 1763, 1849, and 75809. Furthermore, the greatest perfect square on this list is 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Calculate 75809 divided by the greatest perfect square from the list of all factors of 75809. We determined above that the greatest perfect square from the list of all factors of 75809 is 1849. Furthermore, 75809 divided by 1849 is 41, therefore B equals 41.

Now we have A and B and can get our answer to 75809 in its simplest radical form as follows:

√75809 = A√B

√75809 = 43√41

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75809 to simplify the square root of 75809 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 75809 and then take the square root of that product. The prime factors that multiply together to make 75809 are 41 x 43 x 43. When we strip out the pairs only, we get 43 x 43 = 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Divide 75809 by the number (A) squared. 43 squared is 1849 and 75809 divided by 1849 is 41. Therefore, B equals 41.

Once again we have A and B and can get our answer to 75809 in its simplest radical form as follows:

√75809 = A√B

√75809 = 43√41

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