Simplify Square Root of 75520

Here we will show you two methods that you can use to simplify the square root of 75520. In other words, we will show you how to find the square root of 75520 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.

√75520 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75520 to simplify the square root of 75520. 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 75520. The factors of 75520 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 59, 64, 80, 118, 128, 160, 236, 256, 295, 320, 472, 590, 640, 944, 1180, 1280, 1888, 2360, 3776, 4720, 7552, 9440, 15104, 18880, 37760, and 75520. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 75520 divided by the greatest perfect square from the list of all factors of 75520. We determined above that the greatest perfect square from the list of all factors of 75520 is 256. Furthermore, 75520 divided by 256 is 295, therefore B equals 295.

Now we have A and B and can get our answer to 75520 in its simplest radical form as follows:

√75520 = A√B

√75520 = 16√295

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75520 to simplify the square root of 75520 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 75520 and then take the square root of that product. The prime factors that multiply together to make 75520 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 59. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 75520 by the number (A) squared. 16 squared is 256 and 75520 divided by 256 is 295. Therefore, B equals 295.

Once again we have A and B and can get our answer to 75520 in its simplest radical form as follows:

√75520 = A√B

√75520 = 16√295

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