Simplify Square Root of 41229

Here we will show you two methods that you can use to simplify the square root of 41229. In other words, we will show you how to find the square root of 41229 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.

√41229 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41229 to simplify the square root of 41229. 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 41229. The factors of 41229 are 1, 3, 9, 27, 81, 509, 1527, 4581, 13743, and 41229. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 41229 divided by the greatest perfect square from the list of all factors of 41229. We determined above that the greatest perfect square from the list of all factors of 41229 is 81. Furthermore, 41229 divided by 81 is 509, therefore B equals 509.

Now we have A and B and can get our answer to 41229 in its simplest radical form as follows:

√41229 = A√B

√41229 = 9√509

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41229 to simplify the square root of 41229 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 41229 and then take the square root of that product. The prime factors that multiply together to make 41229 are 3 x 3 x 3 x 3 x 509. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 41229 by the number (A) squared. 9 squared is 81 and 41229 divided by 81 is 509. Therefore, B equals 509.

Once again we have A and B and can get our answer to 41229 in its simplest radical form as follows:

√41229 = A√B

√41229 = 9√509

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Simplify Square Root of 41230
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