Simplify Square Root of 65532

Here we will show you two methods that you can use to simplify the square root of 65532. In other words, we will show you how to find the square root of 65532 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.

√65532 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65532 to simplify the square root of 65532. 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 65532. The factors of 65532 are 1, 2, 3, 4, 6, 12, 43, 86, 127, 129, 172, 254, 258, 381, 508, 516, 762, 1524, 5461, 10922, 16383, 21844, 32766, and 65532. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 65532 divided by the greatest perfect square from the list of all factors of 65532. We determined above that the greatest perfect square from the list of all factors of 65532 is 4. Furthermore, 65532 divided by 4 is 16383, therefore B equals 16383.

Now we have A and B and can get our answer to 65532 in its simplest radical form as follows:

√65532 = A√B

√65532 = 2√16383

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65532 to simplify the square root of 65532 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 65532 and then take the square root of that product. The prime factors that multiply together to make 65532 are 2 x 2 x 3 x 43 x 127. 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 65532 by the number (A) squared. 2 squared is 4 and 65532 divided by 4 is 16383. Therefore, B equals 16383.

Once again we have A and B and can get our answer to 65532 in its simplest radical form as follows:

√65532 = A√B

√65532 = 2√16383

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Simplify Square Root of 65533
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