Simplify Square Root of 49125

Here we will show you two methods that you can use to simplify the square root of 49125. In other words, we will show you how to find the square root of 49125 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.

√49125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49125 to simplify the square root of 49125. 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 49125. The factors of 49125 are 1, 3, 5, 15, 25, 75, 125, 131, 375, 393, 655, 1965, 3275, 9825, 16375, and 49125. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 49125 divided by the greatest perfect square from the list of all factors of 49125. We determined above that the greatest perfect square from the list of all factors of 49125 is 25. Furthermore, 49125 divided by 25 is 1965, therefore B equals 1965.

Now we have A and B and can get our answer to 49125 in its simplest radical form as follows:

√49125 = A√B

√49125 = 5√1965

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49125 to simplify the square root of 49125 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 49125 and then take the square root of that product. The prime factors that multiply together to make 49125 are 3 x 5 x 5 x 5 x 131. 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 49125 by the number (A) squared. 5 squared is 25 and 49125 divided by 25 is 1965. Therefore, B equals 1965.

Once again we have A and B and can get our answer to 49125 in its simplest radical form as follows:

√49125 = A√B

√49125 = 5√1965

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

Simplify Square Root of 49126
Here is the next square root on our list that we have simplifed for you.