Simplify Square Root of 17672

Here we will show you two methods that you can use to simplify the square root of 17672. In other words, we will show you how to find the square root of 17672 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.

√17672 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 17672 to simplify the square root of 17672. 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 17672. The factors of 17672 are 1, 2, 4, 8, 47, 94, 188, 376, 2209, 4418, 8836, and 17672. Furthermore, the greatest perfect square on this list is 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Calculate 17672 divided by the greatest perfect square from the list of all factors of 17672. We determined above that the greatest perfect square from the list of all factors of 17672 is 8836. Furthermore, 17672 divided by 8836 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 17672 in its simplest radical form as follows:

√17672 = A√B

√17672 = 94√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 17672 to simplify the square root of 17672 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 17672 and then take the square root of that product. The prime factors that multiply together to make 17672 are 2 x 2 x 2 x 47 x 47. When we strip out the pairs only, we get 2 x 2 x 47 x 47 = 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Divide 17672 by the number (A) squared. 94 squared is 8836 and 17672 divided by 8836 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 17672 in its simplest radical form as follows:

√17672 = A√B

√17672 = 94√2

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Simplify Square Root of 17673
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