Simplify Square Root of 43168

Here we will show you two methods that you can use to simplify the square root of 43168. In other words, we will show you how to find the square root of 43168 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.

√43168 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43168 to simplify the square root of 43168. 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 43168. The factors of 43168 are 1, 2, 4, 8, 16, 19, 32, 38, 71, 76, 142, 152, 284, 304, 568, 608, 1136, 1349, 2272, 2698, 5396, 10792, 21584, and 43168. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 43168 divided by the greatest perfect square from the list of all factors of 43168. We determined above that the greatest perfect square from the list of all factors of 43168 is 16. Furthermore, 43168 divided by 16 is 2698, therefore B equals 2698.

Now we have A and B and can get our answer to 43168 in its simplest radical form as follows:

√43168 = A√B

√43168 = 4√2698

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43168 to simplify the square root of 43168 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 43168 and then take the square root of that product. The prime factors that multiply together to make 43168 are 2 x 2 x 2 x 2 x 2 x 19 x 71. 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 43168 by the number (A) squared. 4 squared is 16 and 43168 divided by 16 is 2698. Therefore, B equals 2698.

Once again we have A and B and can get our answer to 43168 in its simplest radical form as follows:

√43168 = A√B

√43168 = 4√2698

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Simplify Square Root of 43169
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