Simplify Square Root of 6016

Here we will show you two methods that you can use to simplify the square root of 6016. In other words, we will show you how to find the square root of 6016 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.

√6016 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 6016 to simplify the square root of 6016. 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 6016. The factors of 6016 are 1, 2, 4, 8, 16, 32, 47, 64, 94, 128, 188, 376, 752, 1504, 3008, and 6016. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 6016 divided by the greatest perfect square from the list of all factors of 6016. We determined above that the greatest perfect square from the list of all factors of 6016 is 64. Furthermore, 6016 divided by 64 is 94, therefore B equals 94.

Now we have A and B and can get our answer to 6016 in its simplest radical form as follows:

√6016 = A√B

√6016 = 8√94

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 6016 to simplify the square root of 6016 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 6016 and then take the square root of that product. The prime factors that multiply together to make 6016 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 6016 by the number (A) squared. 8 squared is 64 and 6016 divided by 64 is 94. Therefore, B equals 94.

Once again we have A and B and can get our answer to 6016 in its simplest radical form as follows:

√6016 = A√B

√6016 = 8√94

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Simplify Square Root of 6017
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