Simplify Square Root of 73636

Here we will show you two methods that you can use to simplify the square root of 73636. In other words, we will show you how to find the square root of 73636 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.

√73636 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73636 to simplify the square root of 73636. 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 73636. The factors of 73636 are 1, 2, 4, 41, 82, 164, 449, 898, 1796, 18409, 36818, and 73636. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 73636 divided by the greatest perfect square from the list of all factors of 73636. We determined above that the greatest perfect square from the list of all factors of 73636 is 4. Furthermore, 73636 divided by 4 is 18409, therefore B equals 18409.

Now we have A and B and can get our answer to 73636 in its simplest radical form as follows:

√73636 = A√B

√73636 = 2√18409

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73636 to simplify the square root of 73636 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 73636 and then take the square root of that product. The prime factors that multiply together to make 73636 are 2 x 2 x 41 x 449. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 73636 by the number (A) squared. 2 squared is 4 and 73636 divided by 4 is 18409. Therefore, B equals 18409.

Once again we have A and B and can get our answer to 73636 in its simplest radical form as follows:

√73636 = A√B

√73636 = 2√18409

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Simplify Square Root of 73637
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