Simplify Square Root of 42140

Here we will show you two methods that you can use to simplify the square root of 42140. In other words, we will show you how to find the square root of 42140 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.

√42140 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42140 to simplify the square root of 42140. 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 42140. The factors of 42140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 43, 49, 70, 86, 98, 140, 172, 196, 215, 245, 301, 430, 490, 602, 860, 980, 1204, 1505, 2107, 3010, 4214, 6020, 8428, 10535, 21070, and 42140. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 42140 divided by the greatest perfect square from the list of all factors of 42140. We determined above that the greatest perfect square from the list of all factors of 42140 is 196. Furthermore, 42140 divided by 196 is 215, therefore B equals 215.

Now we have A and B and can get our answer to 42140 in its simplest radical form as follows:

√42140 = A√B

√42140 = 14√215

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42140 to simplify the square root of 42140 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 42140 and then take the square root of that product. The prime factors that multiply together to make 42140 are 2 x 2 x 5 x 7 x 7 x 43. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 42140 by the number (A) squared. 14 squared is 196 and 42140 divided by 196 is 215. Therefore, B equals 215.

Once again we have A and B and can get our answer to 42140 in its simplest radical form as follows:

√42140 = A√B

√42140 = 14√215

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