Simplify Square Root of 73152

Here we will show you two methods that you can use to simplify the square root of 73152. In other words, we will show you how to find the square root of 73152 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.

√73152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73152 to simplify the square root of 73152. 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 73152. The factors of 73152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 127, 144, 192, 254, 288, 381, 508, 576, 762, 1016, 1143, 1524, 2032, 2286, 3048, 4064, 4572, 6096, 8128, 9144, 12192, 18288, 24384, 36576, and 73152. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 73152 divided by the greatest perfect square from the list of all factors of 73152. We determined above that the greatest perfect square from the list of all factors of 73152 is 576. Furthermore, 73152 divided by 576 is 127, therefore B equals 127.

Now we have A and B and can get our answer to 73152 in its simplest radical form as follows:

√73152 = A√B

√73152 = 24√127

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73152 to simplify the square root of 73152 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 73152 and then take the square root of that product. The prime factors that multiply together to make 73152 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 127. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 73152 by the number (A) squared. 24 squared is 576 and 73152 divided by 576 is 127. Therefore, B equals 127.

Once again we have A and B and can get our answer to 73152 in its simplest radical form as follows:

√73152 = A√B

√73152 = 24√127

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