Simplify Square Root of 9248

Here we will show you two methods that you can use to simplify the square root of 9248. In other words, we will show you how to find the square root of 9248 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.

√9248 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9248 to simplify the square root of 9248. 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 9248. The factors of 9248 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 289, 544, 578, 1156, 2312, 4624, and 9248. Furthermore, the greatest perfect square on this list is 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Calculate 9248 divided by the greatest perfect square from the list of all factors of 9248. We determined above that the greatest perfect square from the list of all factors of 9248 is 4624. Furthermore, 9248 divided by 4624 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 9248 in its simplest radical form as follows:

√9248 = A√B

√9248 = 68√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9248 to simplify the square root of 9248 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 9248 and then take the square root of that product. The prime factors that multiply together to make 9248 are 2 x 2 x 2 x 2 x 2 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 17 x 17 = 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Divide 9248 by the number (A) squared. 68 squared is 4624 and 9248 divided by 4624 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 9248 in its simplest radical form as follows:

√9248 = A√B

√9248 = 68√2

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Simplify Square Root of 9249
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