Simplify Square Root of 42419

Here we will show you two methods that you can use to simplify the square root of 42419. In other words, we will show you how to find the square root of 42419 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.

√42419 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42419 to simplify the square root of 42419. 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 42419. The factors of 42419 are 1, 13, 169, 251, 3263, and 42419. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 42419 divided by the greatest perfect square from the list of all factors of 42419. We determined above that the greatest perfect square from the list of all factors of 42419 is 169. Furthermore, 42419 divided by 169 is 251, therefore B equals 251.

Now we have A and B and can get our answer to 42419 in its simplest radical form as follows:

√42419 = A√B

√42419 = 13√251

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42419 to simplify the square root of 42419 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 42419 and then take the square root of that product. The prime factors that multiply together to make 42419 are 13 x 13 x 251. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 42419 by the number (A) squared. 13 squared is 169 and 42419 divided by 169 is 251. Therefore, B equals 251.

Once again we have A and B and can get our answer to 42419 in its simplest radical form as follows:

√42419 = A√B

√42419 = 13√251

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 42420
Here is the next square root on our list that we have simplifed for you.