Simplify Square Root of 34006

Here we will show you two methods that you can use to simplify the square root of 34006. In other words, we will show you how to find the square root of 34006 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.

√34006 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34006 to simplify the square root of 34006. 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 34006. The factors of 34006 are 1, 2, 7, 14, 49, 98, 347, 694, 2429, 4858, 17003, and 34006. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 34006 divided by the greatest perfect square from the list of all factors of 34006. We determined above that the greatest perfect square from the list of all factors of 34006 is 49. Furthermore, 34006 divided by 49 is 694, therefore B equals 694.

Now we have A and B and can get our answer to 34006 in its simplest radical form as follows:

√34006 = A√B

√34006 = 7√694

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34006 to simplify the square root of 34006 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 34006 and then take the square root of that product. The prime factors that multiply together to make 34006 are 2 x 7 x 7 x 347. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 34006 by the number (A) squared. 7 squared is 49 and 34006 divided by 49 is 694. Therefore, B equals 694.

Once again we have A and B and can get our answer to 34006 in its simplest radical form as follows:

√34006 = A√B

√34006 = 7√694

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Simplify Square Root of 34007
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