Simplify Square Root of 48975

Here we will show you two methods that you can use to simplify the square root of 48975. In other words, we will show you how to find the square root of 48975 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.

√48975 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48975 to simplify the square root of 48975. 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 48975. The factors of 48975 are 1, 3, 5, 15, 25, 75, 653, 1959, 3265, 9795, 16325, and 48975. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 48975 divided by the greatest perfect square from the list of all factors of 48975. We determined above that the greatest perfect square from the list of all factors of 48975 is 25. Furthermore, 48975 divided by 25 is 1959, therefore B equals 1959.

Now we have A and B and can get our answer to 48975 in its simplest radical form as follows:

√48975 = A√B

√48975 = 5√1959

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48975 to simplify the square root of 48975 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 48975 and then take the square root of that product. The prime factors that multiply together to make 48975 are 3 x 5 x 5 x 653. 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 48975 by the number (A) squared. 5 squared is 25 and 48975 divided by 25 is 1959. Therefore, B equals 1959.

Once again we have A and B and can get our answer to 48975 in its simplest radical form as follows:

√48975 = A√B

√48975 = 5√1959

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Simplify Square Root of 48976
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