Simplify Square Root of 47425

Here we will show you two methods that you can use to simplify the square root of 47425. In other words, we will show you how to find the square root of 47425 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.

√47425 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47425 to simplify the square root of 47425. 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 47425. The factors of 47425 are 1, 5, 7, 25, 35, 175, 271, 1355, 1897, 6775, 9485, and 47425. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 47425 divided by the greatest perfect square from the list of all factors of 47425. We determined above that the greatest perfect square from the list of all factors of 47425 is 25. Furthermore, 47425 divided by 25 is 1897, therefore B equals 1897.

Now we have A and B and can get our answer to 47425 in its simplest radical form as follows:

√47425 = A√B

√47425 = 5√1897

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47425 to simplify the square root of 47425 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 47425 and then take the square root of that product. The prime factors that multiply together to make 47425 are 5 x 5 x 7 x 271. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 47425 by the number (A) squared. 5 squared is 25 and 47425 divided by 25 is 1897. Therefore, B equals 1897.

Once again we have A and B and can get our answer to 47425 in its simplest radical form as follows:

√47425 = A√B

√47425 = 5√1897

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

Simplify Square Root of 47426
Here is the next square root on our list that we have simplifed for you.