Simplify Square Root of 69252

Here we will show you two methods that you can use to simplify the square root of 69252. In other words, we will show you how to find the square root of 69252 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.

√69252 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69252 to simplify the square root of 69252. 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 69252. The factors of 69252 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 199, 348, 398, 597, 796, 1194, 2388, 5771, 11542, 17313, 23084, 34626, and 69252. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 69252 divided by the greatest perfect square from the list of all factors of 69252. We determined above that the greatest perfect square from the list of all factors of 69252 is 4. Furthermore, 69252 divided by 4 is 17313, therefore B equals 17313.

Now we have A and B and can get our answer to 69252 in its simplest radical form as follows:

√69252 = A√B

√69252 = 2√17313

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69252 to simplify the square root of 69252 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 69252 and then take the square root of that product. The prime factors that multiply together to make 69252 are 2 x 2 x 3 x 29 x 199. 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 69252 by the number (A) squared. 2 squared is 4 and 69252 divided by 4 is 17313. Therefore, B equals 17313.

Once again we have A and B and can get our answer to 69252 in its simplest radical form as follows:

√69252 = A√B

√69252 = 2√17313

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Simplify Square Root of 69253
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