Simplify Square Root of 60492

Here we will show you two methods that you can use to simplify the square root of 60492. In other words, we will show you how to find the square root of 60492 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.

√60492 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60492 to simplify the square root of 60492. 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 60492. The factors of 60492 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852, 5041, 10082, 15123, 20164, 30246, and 60492. Furthermore, the greatest perfect square on this list is 20164 and the square root of 20164 is 142. Therefore, A equals 142.

B = Calculate 60492 divided by the greatest perfect square from the list of all factors of 60492. We determined above that the greatest perfect square from the list of all factors of 60492 is 20164. Furthermore, 60492 divided by 20164 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 60492 in its simplest radical form as follows:

√60492 = A√B

√60492 = 142√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60492 to simplify the square root of 60492 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 60492 and then take the square root of that product. The prime factors that multiply together to make 60492 are 2 x 2 x 3 x 71 x 71. When we strip out the pairs only, we get 2 x 2 x 71 x 71 = 20164 and the square root of 20164 is 142. Therefore, A equals 142.

B = Divide 60492 by the number (A) squared. 142 squared is 20164 and 60492 divided by 20164 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 60492 in its simplest radical form as follows:

√60492 = A√B

√60492 = 142√3

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Simplify Square Root of 60493
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