Simplify Square Root of 13454

Here we will show you two methods that you can use to simplify the square root of 13454. In other words, we will show you how to find the square root of 13454 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.

√13454 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13454 to simplify the square root of 13454. 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 13454. The factors of 13454 are 1, 2, 7, 14, 31, 62, 217, 434, 961, 1922, 6727, and 13454. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 13454 divided by the greatest perfect square from the list of all factors of 13454. We determined above that the greatest perfect square from the list of all factors of 13454 is 961. Furthermore, 13454 divided by 961 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 13454 in its simplest radical form as follows:

√13454 = A√B

√13454 = 31√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13454 to simplify the square root of 13454 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 13454 and then take the square root of that product. The prime factors that multiply together to make 13454 are 2 x 7 x 31 x 31. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 13454 by the number (A) squared. 31 squared is 961 and 13454 divided by 961 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 13454 in its simplest radical form as follows:

√13454 = A√B

√13454 = 31√14

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Simplify Square Root of 13455
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