Simplify Square Root of 10693

Here we will show you two methods that you can use to simplify the square root of 10693. In other words, we will show you how to find the square root of 10693 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.

√10693 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10693 to simplify the square root of 10693. 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 10693. The factors of 10693 are 1, 17, 37, 289, 629, and 10693. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 10693 divided by the greatest perfect square from the list of all factors of 10693. We determined above that the greatest perfect square from the list of all factors of 10693 is 289. Furthermore, 10693 divided by 289 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 10693 in its simplest radical form as follows:

√10693 = A√B

√10693 = 17√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10693 to simplify the square root of 10693 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 10693 and then take the square root of that product. The prime factors that multiply together to make 10693 are 17 x 17 x 37. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 10693 by the number (A) squared. 17 squared is 289 and 10693 divided by 289 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 10693 in its simplest radical form as follows:

√10693 = A√B

√10693 = 17√37

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