Simplify Square Root of 69032

Here we will show you two methods that you can use to simplify the square root of 69032. In other words, we will show you how to find the square root of 69032 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.

√69032 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69032 to simplify the square root of 69032. 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 69032. The factors of 69032 are 1, 2, 4, 8, 8629, 17258, 34516, and 69032. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 69032 divided by the greatest perfect square from the list of all factors of 69032. We determined above that the greatest perfect square from the list of all factors of 69032 is 4. Furthermore, 69032 divided by 4 is 17258, therefore B equals 17258.

Now we have A and B and can get our answer to 69032 in its simplest radical form as follows:

√69032 = A√B

√69032 = 2√17258

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69032 to simplify the square root of 69032 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 69032 and then take the square root of that product. The prime factors that multiply together to make 69032 are 2 x 2 x 2 x 8629. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 69032 by the number (A) squared. 2 squared is 4 and 69032 divided by 4 is 17258. Therefore, B equals 17258.

Once again we have A and B and can get our answer to 69032 in its simplest radical form as follows:

√69032 = A√B

√69032 = 2√17258

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Simplify Square Root of 69033
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