Simplify Square Root of 84672

Here we will show you two methods that you can use to simplify the square root of 84672. In other words, we will show you how to find the square root of 84672 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.

√84672 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84672 to simplify the square root of 84672. 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 84672. The factors of 84672 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 49, 54, 56, 63, 64, 72, 84, 96, 98, 108, 112, 126, 144, 147, 168, 189, 192, 196, 216, 224, 252, 288, 294, 336, 378, 392, 432, 441, 448, 504, 576, 588, 672, 756, 784, 864, 882, 1008, 1176, 1323, 1344, 1512, 1568, 1728, 1764, 2016, 2352, 2646, 3024, 3136, 3528, 4032, 4704, 5292, 6048, 7056, 9408, 10584, 12096, 14112, 21168, 28224, 42336, and 84672. Furthermore, the greatest perfect square on this list is 28224 and the square root of 28224 is 168. Therefore, A equals 168.

B = Calculate 84672 divided by the greatest perfect square from the list of all factors of 84672. We determined above that the greatest perfect square from the list of all factors of 84672 is 28224. Furthermore, 84672 divided by 28224 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 84672 in its simplest radical form as follows:

√84672 = A√B

√84672 = 168√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84672 to simplify the square root of 84672 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 84672 and then take the square root of that product. The prime factors that multiply together to make 84672 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7 = 28224 and the square root of 28224 is 168. Therefore, A equals 168.

B = Divide 84672 by the number (A) squared. 168 squared is 28224 and 84672 divided by 28224 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 84672 in its simplest radical form as follows:

√84672 = A√B

√84672 = 168√3

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Simplify Square Root of 84673
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