Simplify Square Root of 69248

Here we will show you two methods that you can use to simplify the square root of 69248. In other words, we will show you how to find the square root of 69248 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.

√69248 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69248 to simplify the square root of 69248. 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 69248. The factors of 69248 are 1, 2, 4, 8, 16, 32, 64, 128, 541, 1082, 2164, 4328, 8656, 17312, 34624, and 69248. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 69248 divided by the greatest perfect square from the list of all factors of 69248. We determined above that the greatest perfect square from the list of all factors of 69248 is 64. Furthermore, 69248 divided by 64 is 1082, therefore B equals 1082.

Now we have A and B and can get our answer to 69248 in its simplest radical form as follows:

√69248 = A√B

√69248 = 8√1082

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69248 to simplify the square root of 69248 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 69248 and then take the square root of that product. The prime factors that multiply together to make 69248 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 541. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 69248 by the number (A) squared. 8 squared is 64 and 69248 divided by 64 is 1082. Therefore, B equals 1082.

Once again we have A and B and can get our answer to 69248 in its simplest radical form as follows:

√69248 = A√B

√69248 = 8√1082

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

Simplify Square Root of 69249
Here is the next square root on our list that we have simplifed for you.