Simplify Square Root of 35672

Here we will show you two methods that you can use to simplify the square root of 35672. In other words, we will show you how to find the square root of 35672 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.

√35672 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35672 to simplify the square root of 35672. 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 35672. The factors of 35672 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 49, 52, 56, 91, 98, 104, 182, 196, 343, 364, 392, 637, 686, 728, 1274, 1372, 2548, 2744, 4459, 5096, 8918, 17836, and 35672. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 35672 divided by the greatest perfect square from the list of all factors of 35672. We determined above that the greatest perfect square from the list of all factors of 35672 is 196. Furthermore, 35672 divided by 196 is 182, therefore B equals 182.

Now we have A and B and can get our answer to 35672 in its simplest radical form as follows:

√35672 = A√B

√35672 = 14√182

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35672 to simplify the square root of 35672 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 35672 and then take the square root of that product. The prime factors that multiply together to make 35672 are 2 x 2 x 2 x 7 x 7 x 7 x 13. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 35672 by the number (A) squared. 14 squared is 196 and 35672 divided by 196 is 182. Therefore, B equals 182.

Once again we have A and B and can get our answer to 35672 in its simplest radical form as follows:

√35672 = A√B

√35672 = 14√182

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Simplify Square Root of 35673
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