Simplify Square Root of 48125

Here we will show you two methods that you can use to simplify the square root of 48125. In other words, we will show you how to find the square root of 48125 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.

√48125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48125 to simplify the square root of 48125. 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 48125. The factors of 48125 are 1, 5, 7, 11, 25, 35, 55, 77, 125, 175, 275, 385, 625, 875, 1375, 1925, 4375, 6875, 9625, and 48125. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 48125 divided by the greatest perfect square from the list of all factors of 48125. We determined above that the greatest perfect square from the list of all factors of 48125 is 625. Furthermore, 48125 divided by 625 is 77, therefore B equals 77.

Now we have A and B and can get our answer to 48125 in its simplest radical form as follows:

√48125 = A√B

√48125 = 25√77

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48125 to simplify the square root of 48125 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 48125 and then take the square root of that product. The prime factors that multiply together to make 48125 are 5 x 5 x 5 x 5 x 7 x 11. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 48125 by the number (A) squared. 25 squared is 625 and 48125 divided by 625 is 77. Therefore, B equals 77.

Once again we have A and B and can get our answer to 48125 in its simplest radical form as follows:

√48125 = A√B

√48125 = 25√77

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Simplify Square Root of 48126
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