Simplify Square Root of 38962

Here we will show you two methods that you can use to simplify the square root of 38962. In other words, we will show you how to find the square root of 38962 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.

√38962 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38962 to simplify the square root of 38962. 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 38962. The factors of 38962 are 1, 2, 7, 11, 14, 22, 23, 46, 77, 121, 154, 161, 242, 253, 322, 506, 847, 1694, 1771, 2783, 3542, 5566, 19481, and 38962. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 38962 divided by the greatest perfect square from the list of all factors of 38962. We determined above that the greatest perfect square from the list of all factors of 38962 is 121. Furthermore, 38962 divided by 121 is 322, therefore B equals 322.

Now we have A and B and can get our answer to 38962 in its simplest radical form as follows:

√38962 = A√B

√38962 = 11√322

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38962 to simplify the square root of 38962 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 38962 and then take the square root of that product. The prime factors that multiply together to make 38962 are 2 x 7 x 11 x 11 x 23. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 38962 by the number (A) squared. 11 squared is 121 and 38962 divided by 121 is 322. Therefore, B equals 322.

Once again we have A and B and can get our answer to 38962 in its simplest radical form as follows:

√38962 = A√B

√38962 = 11√322

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Simplify Square Root of 38963
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