Simplify Square Root of 14975

Here we will show you two methods that you can use to simplify the square root of 14975. In other words, we will show you how to find the square root of 14975 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.

√14975 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 14975 to simplify the square root of 14975. 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 14975. The factors of 14975 are 1, 5, 25, 599, 2995, and 14975. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 14975 divided by the greatest perfect square from the list of all factors of 14975. We determined above that the greatest perfect square from the list of all factors of 14975 is 25. Furthermore, 14975 divided by 25 is 599, therefore B equals 599.

Now we have A and B and can get our answer to 14975 in its simplest radical form as follows:

√14975 = A√B

√14975 = 5√599

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 14975 to simplify the square root of 14975 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 14975 and then take the square root of that product. The prime factors that multiply together to make 14975 are 5 x 5 x 599. 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 14975 by the number (A) squared. 5 squared is 25 and 14975 divided by 25 is 599. Therefore, B equals 599.

Once again we have A and B and can get our answer to 14975 in its simplest radical form as follows:

√14975 = A√B

√14975 = 5√599

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Simplify Square Root of 14976
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