Simplify Square Root of 54075

Here we will show you two methods that you can use to simplify the square root of 54075. In other words, we will show you how to find the square root of 54075 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.

√54075 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54075 to simplify the square root of 54075. 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 54075. The factors of 54075 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 103, 105, 175, 309, 515, 525, 721, 1545, 2163, 2575, 3605, 7725, 10815, 18025, and 54075. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 54075 divided by the greatest perfect square from the list of all factors of 54075. We determined above that the greatest perfect square from the list of all factors of 54075 is 25. Furthermore, 54075 divided by 25 is 2163, therefore B equals 2163.

Now we have A and B and can get our answer to 54075 in its simplest radical form as follows:

√54075 = A√B

√54075 = 5√2163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54075 to simplify the square root of 54075 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 54075 and then take the square root of that product. The prime factors that multiply together to make 54075 are 3 x 5 x 5 x 7 x 103. 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 54075 by the number (A) squared. 5 squared is 25 and 54075 divided by 25 is 2163. Therefore, B equals 2163.

Once again we have A and B and can get our answer to 54075 in its simplest radical form as follows:

√54075 = A√B

√54075 = 5√2163

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Simplify Square Root of 54076
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