Simplify Square Root of 69849

Here we will show you two methods that you can use to simplify the square root of 69849. In other words, we will show you how to find the square root of 69849 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.

√69849 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69849 to simplify the square root of 69849. 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 69849. The factors of 69849 are 1, 3, 9, 13, 27, 39, 117, 199, 351, 597, 1791, 2587, 5373, 7761, 23283, and 69849. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 69849 divided by the greatest perfect square from the list of all factors of 69849. We determined above that the greatest perfect square from the list of all factors of 69849 is 9. Furthermore, 69849 divided by 9 is 7761, therefore B equals 7761.

Now we have A and B and can get our answer to 69849 in its simplest radical form as follows:

√69849 = A√B

√69849 = 3√7761

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69849 to simplify the square root of 69849 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 69849 and then take the square root of that product. The prime factors that multiply together to make 69849 are 3 x 3 x 3 x 13 x 199. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 69849 by the number (A) squared. 3 squared is 9 and 69849 divided by 9 is 7761. Therefore, B equals 7761.

Once again we have A and B and can get our answer to 69849 in its simplest radical form as follows:

√69849 = A√B

√69849 = 3√7761

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Simplify Square Root of 69850
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