Simplify Square Root of 48675

Here we will show you two methods that you can use to simplify the square root of 48675. In other words, we will show you how to find the square root of 48675 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.

√48675 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48675 to simplify the square root of 48675. 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 48675. The factors of 48675 are 1, 3, 5, 11, 15, 25, 33, 55, 59, 75, 165, 177, 275, 295, 649, 825, 885, 1475, 1947, 3245, 4425, 9735, 16225, and 48675. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 48675 divided by the greatest perfect square from the list of all factors of 48675. We determined above that the greatest perfect square from the list of all factors of 48675 is 25. Furthermore, 48675 divided by 25 is 1947, therefore B equals 1947.

Now we have A and B and can get our answer to 48675 in its simplest radical form as follows:

√48675 = A√B

√48675 = 5√1947

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48675 to simplify the square root of 48675 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 48675 and then take the square root of that product. The prime factors that multiply together to make 48675 are 3 x 5 x 5 x 11 x 59. 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 48675 by the number (A) squared. 5 squared is 25 and 48675 divided by 25 is 1947. Therefore, B equals 1947.

Once again we have A and B and can get our answer to 48675 in its simplest radical form as follows:

√48675 = A√B

√48675 = 5√1947

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Simplify Square Root of 48676
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