Simplify Square Root of 83582

Here we will show you two methods that you can use to simplify the square root of 83582. In other words, we will show you how to find the square root of 83582 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.

√83582 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83582 to simplify the square root of 83582. 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 83582. The factors of 83582 are 1, 2, 23, 46, 79, 158, 529, 1058, 1817, 3634, 41791, and 83582. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 83582 divided by the greatest perfect square from the list of all factors of 83582. We determined above that the greatest perfect square from the list of all factors of 83582 is 529. Furthermore, 83582 divided by 529 is 158, therefore B equals 158.

Now we have A and B and can get our answer to 83582 in its simplest radical form as follows:

√83582 = A√B

√83582 = 23√158

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83582 to simplify the square root of 83582 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 83582 and then take the square root of that product. The prime factors that multiply together to make 83582 are 2 x 23 x 23 x 79. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 83582 by the number (A) squared. 23 squared is 529 and 83582 divided by 529 is 158. Therefore, B equals 158.

Once again we have A and B and can get our answer to 83582 in its simplest radical form as follows:

√83582 = A√B

√83582 = 23√158

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Simplify Square Root of 83583
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