Simplify Square Root of 41152

Here we will show you two methods that you can use to simplify the square root of 41152. In other words, we will show you how to find the square root of 41152 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.

√41152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41152 to simplify the square root of 41152. 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 41152. The factors of 41152 are 1, 2, 4, 8, 16, 32, 64, 643, 1286, 2572, 5144, 10288, 20576, and 41152. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 41152 divided by the greatest perfect square from the list of all factors of 41152. We determined above that the greatest perfect square from the list of all factors of 41152 is 64. Furthermore, 41152 divided by 64 is 643, therefore B equals 643.

Now we have A and B and can get our answer to 41152 in its simplest radical form as follows:

√41152 = A√B

√41152 = 8√643

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41152 to simplify the square root of 41152 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 41152 and then take the square root of that product. The prime factors that multiply together to make 41152 are 2 x 2 x 2 x 2 x 2 x 2 x 643. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 41152 by the number (A) squared. 8 squared is 64 and 41152 divided by 64 is 643. Therefore, B equals 643.

Once again we have A and B and can get our answer to 41152 in its simplest radical form as follows:

√41152 = A√B

√41152 = 8√643

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Simplify Square Root of 41153
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