Simplify Square Root of 42201

Here we will show you two methods that you can use to simplify the square root of 42201. In other words, we will show you how to find the square root of 42201 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.

√42201 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 42201 to simplify the square root of 42201. 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 42201. The factors of 42201 are 1, 3, 9, 27, 81, 521, 1563, 4689, 14067, and 42201. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 42201 divided by the greatest perfect square from the list of all factors of 42201. We determined above that the greatest perfect square from the list of all factors of 42201 is 81. Furthermore, 42201 divided by 81 is 521, therefore B equals 521.

Now we have A and B and can get our answer to 42201 in its simplest radical form as follows:

√42201 = A√B

√42201 = 9√521

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 42201 to simplify the square root of 42201 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 42201 and then take the square root of that product. The prime factors that multiply together to make 42201 are 3 x 3 x 3 x 3 x 521. 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 42201 by the number (A) squared. 9 squared is 81 and 42201 divided by 81 is 521. Therefore, B equals 521.

Once again we have A and B and can get our answer to 42201 in its simplest radical form as follows:

√42201 = A√B

√42201 = 9√521

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Simplify Square Root of 42202
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