Simplify Square Root of 60417

Here we will show you two methods that you can use to simplify the square root of 60417. In other words, we will show you how to find the square root of 60417 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.

√60417 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60417 to simplify the square root of 60417. 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 60417. The factors of 60417 are 1, 3, 7, 9, 21, 49, 63, 137, 147, 411, 441, 959, 1233, 2877, 6713, 8631, 20139, and 60417. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 60417 divided by the greatest perfect square from the list of all factors of 60417. We determined above that the greatest perfect square from the list of all factors of 60417 is 441. Furthermore, 60417 divided by 441 is 137, therefore B equals 137.

Now we have A and B and can get our answer to 60417 in its simplest radical form as follows:

√60417 = A√B

√60417 = 21√137

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60417 to simplify the square root of 60417 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 60417 and then take the square root of that product. The prime factors that multiply together to make 60417 are 3 x 3 x 7 x 7 x 137. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 60417 by the number (A) squared. 21 squared is 441 and 60417 divided by 441 is 137. Therefore, B equals 137.

Once again we have A and B and can get our answer to 60417 in its simplest radical form as follows:

√60417 = A√B

√60417 = 21√137

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Simplify Square Root of 60418
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