Simplify Square Root of 32258

Here we will show you two methods that you can use to simplify the square root of 32258. In other words, we will show you how to find the square root of 32258 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.

√32258 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32258 to simplify the square root of 32258. 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 32258. The factors of 32258 are 1, 2, 127, 254, 16129, and 32258. Furthermore, the greatest perfect square on this list is 16129 and the square root of 16129 is 127. Therefore, A equals 127.

B = Calculate 32258 divided by the greatest perfect square from the list of all factors of 32258. We determined above that the greatest perfect square from the list of all factors of 32258 is 16129. Furthermore, 32258 divided by 16129 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 32258 in its simplest radical form as follows:

√32258 = A√B

√32258 = 127√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32258 to simplify the square root of 32258 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 32258 and then take the square root of that product. The prime factors that multiply together to make 32258 are 2 x 127 x 127. When we strip out the pairs only, we get 127 x 127 = 16129 and the square root of 16129 is 127. Therefore, A equals 127.

B = Divide 32258 by the number (A) squared. 127 squared is 16129 and 32258 divided by 16129 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 32258 in its simplest radical form as follows:

√32258 = A√B

√32258 = 127√2

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Simplify Square Root of 32259
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