Simplify Square Root of 67664

Here we will show you two methods that you can use to simplify the square root of 67664. In other words, we will show you how to find the square root of 67664 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.

√67664 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 67664 to simplify the square root of 67664. 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 67664. The factors of 67664 are 1, 2, 4, 8, 16, 4229, 8458, 16916, 33832, and 67664. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 67664 divided by the greatest perfect square from the list of all factors of 67664. We determined above that the greatest perfect square from the list of all factors of 67664 is 16. Furthermore, 67664 divided by 16 is 4229, therefore B equals 4229.

Now we have A and B and can get our answer to 67664 in its simplest radical form as follows:

√67664 = A√B

√67664 = 4√4229

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 67664 to simplify the square root of 67664 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 67664 and then take the square root of that product. The prime factors that multiply together to make 67664 are 2 x 2 x 2 x 2 x 4229. 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 67664 by the number (A) squared. 4 squared is 16 and 67664 divided by 16 is 4229. Therefore, B equals 4229.

Once again we have A and B and can get our answer to 67664 in its simplest radical form as follows:

√67664 = A√B

√67664 = 4√4229

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Simplify Square Root of 67665
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