Simplify Square Root of 14762

Here we will show you two methods that you can use to simplify the square root of 14762. In other words, we will show you how to find the square root of 14762 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.

√14762 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 14762 to simplify the square root of 14762. 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 14762. The factors of 14762 are 1, 2, 11, 22, 61, 121, 122, 242, 671, 1342, 7381, and 14762. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 14762 divided by the greatest perfect square from the list of all factors of 14762. We determined above that the greatest perfect square from the list of all factors of 14762 is 121. Furthermore, 14762 divided by 121 is 122, therefore B equals 122.

Now we have A and B and can get our answer to 14762 in its simplest radical form as follows:

√14762 = A√B

√14762 = 11√122

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 14762 to simplify the square root of 14762 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 14762 and then take the square root of that product. The prime factors that multiply together to make 14762 are 2 x 11 x 11 x 61. 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 14762 by the number (A) squared. 11 squared is 121 and 14762 divided by 121 is 122. Therefore, B equals 122.

Once again we have A and B and can get our answer to 14762 in its simplest radical form as follows:

√14762 = A√B

√14762 = 11√122

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Simplify Square Root of 14763
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