Simplify Square Root of 59168

Here we will show you two methods that you can use to simplify the square root of 59168. In other words, we will show you how to find the square root of 59168 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.

√59168 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59168 to simplify the square root of 59168. 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 59168. The factors of 59168 are 1, 2, 4, 8, 16, 32, 43, 86, 172, 344, 688, 1376, 1849, 3698, 7396, 14792, 29584, and 59168. Furthermore, the greatest perfect square on this list is 29584 and the square root of 29584 is 172. Therefore, A equals 172.

B = Calculate 59168 divided by the greatest perfect square from the list of all factors of 59168. We determined above that the greatest perfect square from the list of all factors of 59168 is 29584. Furthermore, 59168 divided by 29584 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 59168 in its simplest radical form as follows:

√59168 = A√B

√59168 = 172√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59168 to simplify the square root of 59168 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 59168 and then take the square root of that product. The prime factors that multiply together to make 59168 are 2 x 2 x 2 x 2 x 2 x 43 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 43 x 43 = 29584 and the square root of 29584 is 172. Therefore, A equals 172.

B = Divide 59168 by the number (A) squared. 172 squared is 29584 and 59168 divided by 29584 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 59168 in its simplest radical form as follows:

√59168 = A√B

√59168 = 172√2

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Simplify Square Root of 59169
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