Simplify Square Root of 83152

Here we will show you two methods that you can use to simplify the square root of 83152. In other words, we will show you how to find the square root of 83152 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.

√83152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83152 to simplify the square root of 83152. 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 83152. The factors of 83152 are 1, 2, 4, 8, 16, 5197, 10394, 20788, 41576, and 83152. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 83152 divided by the greatest perfect square from the list of all factors of 83152. We determined above that the greatest perfect square from the list of all factors of 83152 is 16. Furthermore, 83152 divided by 16 is 5197, therefore B equals 5197.

Now we have A and B and can get our answer to 83152 in its simplest radical form as follows:

√83152 = A√B

√83152 = 4√5197

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83152 to simplify the square root of 83152 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 83152 and then take the square root of that product. The prime factors that multiply together to make 83152 are 2 x 2 x 2 x 2 x 5197. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 83152 by the number (A) squared. 4 squared is 16 and 83152 divided by 16 is 5197. Therefore, B equals 5197.

Once again we have A and B and can get our answer to 83152 in its simplest radical form as follows:

√83152 = A√B

√83152 = 4√5197

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Simplify Square Root of 83153
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