Simplify Square Root of 75647

Here we will show you two methods that you can use to simplify the square root of 75647. In other words, we will show you how to find the square root of 75647 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.

√75647 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75647 to simplify the square root of 75647. 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 75647. The factors of 75647 are 1, 11, 13, 23, 143, 253, 299, 529, 3289, 5819, 6877, and 75647. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 75647 divided by the greatest perfect square from the list of all factors of 75647. We determined above that the greatest perfect square from the list of all factors of 75647 is 529. Furthermore, 75647 divided by 529 is 143, therefore B equals 143.

Now we have A and B and can get our answer to 75647 in its simplest radical form as follows:

√75647 = A√B

√75647 = 23√143

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75647 to simplify the square root of 75647 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 75647 and then take the square root of that product. The prime factors that multiply together to make 75647 are 11 x 13 x 23 x 23. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 75647 by the number (A) squared. 23 squared is 529 and 75647 divided by 529 is 143. Therefore, B equals 143.

Once again we have A and B and can get our answer to 75647 in its simplest radical form as follows:

√75647 = A√B

√75647 = 23√143

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 75648
Here is the next square root on our list that we have simplifed for you.