Simplify Square Root of 96148

Here we will show you two methods that you can use to simplify the square root of 96148. In other words, we will show you how to find the square root of 96148 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.

√96148 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96148 to simplify the square root of 96148. 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 96148. The factors of 96148 are 1, 2, 4, 13, 26, 43, 52, 86, 172, 559, 1118, 1849, 2236, 3698, 7396, 24037, 48074, and 96148. Furthermore, the greatest perfect square on this list is 7396 and the square root of 7396 is 86. Therefore, A equals 86.

B = Calculate 96148 divided by the greatest perfect square from the list of all factors of 96148. We determined above that the greatest perfect square from the list of all factors of 96148 is 7396. Furthermore, 96148 divided by 7396 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 96148 in its simplest radical form as follows:

√96148 = A√B

√96148 = 86√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96148 to simplify the square root of 96148 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 96148 and then take the square root of that product. The prime factors that multiply together to make 96148 are 2 x 2 x 13 x 43 x 43. When we strip out the pairs only, we get 2 x 2 x 43 x 43 = 7396 and the square root of 7396 is 86. Therefore, A equals 86.

B = Divide 96148 by the number (A) squared. 86 squared is 7396 and 96148 divided by 7396 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 96148 in its simplest radical form as follows:

√96148 = A√B

√96148 = 86√13

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Simplify Square Root of 96149
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