Simplify Square Root of 43821

Here we will show you two methods that you can use to simplify the square root of 43821. In other words, we will show you how to find the square root of 43821 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.

√43821 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43821 to simplify the square root of 43821. 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 43821. The factors of 43821 are 1, 3, 9, 27, 81, 541, 1623, 4869, 14607, and 43821. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 43821 divided by the greatest perfect square from the list of all factors of 43821. We determined above that the greatest perfect square from the list of all factors of 43821 is 81. Furthermore, 43821 divided by 81 is 541, therefore B equals 541.

Now we have A and B and can get our answer to 43821 in its simplest radical form as follows:

√43821 = A√B

√43821 = 9√541

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43821 to simplify the square root of 43821 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 43821 and then take the square root of that product. The prime factors that multiply together to make 43821 are 3 x 3 x 3 x 3 x 541. 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 43821 by the number (A) squared. 9 squared is 81 and 43821 divided by 81 is 541. Therefore, B equals 541.

Once again we have A and B and can get our answer to 43821 in its simplest radical form as follows:

√43821 = A√B

√43821 = 9√541

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Simplify Square Root of 43822
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