Simplify Square Root of 98304

Here we will show you two methods that you can use to simplify the square root of 98304. In other words, we will show you how to find the square root of 98304 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.

√98304 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 98304 to simplify the square root of 98304. 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 98304. The factors of 98304 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, and 98304. Furthermore, the greatest perfect square on this list is 16384 and the square root of 16384 is 128. Therefore, A equals 128.

B = Calculate 98304 divided by the greatest perfect square from the list of all factors of 98304. We determined above that the greatest perfect square from the list of all factors of 98304 is 16384. Furthermore, 98304 divided by 16384 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 98304 in its simplest radical form as follows:

√98304 = A√B

√98304 = 128√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 98304 to simplify the square root of 98304 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 98304 and then take the square root of that product. The prime factors that multiply together to make 98304 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 16384 and the square root of 16384 is 128. Therefore, A equals 128.

B = Divide 98304 by the number (A) squared. 128 squared is 16384 and 98304 divided by 16384 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 98304 in its simplest radical form as follows:

√98304 = A√B

√98304 = 128√6

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