Simplify Square Root of 69008

Here we will show you two methods that you can use to simplify the square root of 69008. In other words, we will show you how to find the square root of 69008 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.

√69008 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69008 to simplify the square root of 69008. 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 69008. The factors of 69008 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 227, 304, 454, 908, 1816, 3632, 4313, 8626, 17252, 34504, and 69008. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 69008 divided by the greatest perfect square from the list of all factors of 69008. We determined above that the greatest perfect square from the list of all factors of 69008 is 16. Furthermore, 69008 divided by 16 is 4313, therefore B equals 4313.

Now we have A and B and can get our answer to 69008 in its simplest radical form as follows:

√69008 = A√B

√69008 = 4√4313

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69008 to simplify the square root of 69008 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 69008 and then take the square root of that product. The prime factors that multiply together to make 69008 are 2 x 2 x 2 x 2 x 19 x 227. 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 69008 by the number (A) squared. 4 squared is 16 and 69008 divided by 16 is 4313. Therefore, B equals 4313.

Once again we have A and B and can get our answer to 69008 in its simplest radical form as follows:

√69008 = A√B

√69008 = 4√4313

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Simplify Square Root of 69009
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