Simplify Square Root of 69024

Here we will show you two methods that you can use to simplify the square root of 69024. In other words, we will show you how to find the square root of 69024 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.

√69024 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69024 to simplify the square root of 69024. 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 69024. The factors of 69024 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 719, 1438, 2157, 2876, 4314, 5752, 8628, 11504, 17256, 23008, 34512, and 69024. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 69024 divided by the greatest perfect square from the list of all factors of 69024. We determined above that the greatest perfect square from the list of all factors of 69024 is 16. Furthermore, 69024 divided by 16 is 4314, therefore B equals 4314.

Now we have A and B and can get our answer to 69024 in its simplest radical form as follows:

√69024 = A√B

√69024 = 4√4314

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69024 to simplify the square root of 69024 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 69024 and then take the square root of that product. The prime factors that multiply together to make 69024 are 2 x 2 x 2 x 2 x 2 x 3 x 719. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 69024 by the number (A) squared. 4 squared is 16 and 69024 divided by 16 is 4314. Therefore, B equals 4314.

Once again we have A and B and can get our answer to 69024 in its simplest radical form as follows:

√69024 = A√B

√69024 = 4√4314

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