Simplify Square Root of 75264

Here we will show you two methods that you can use to simplify the square root of 75264. In other words, we will show you how to find the square root of 75264 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.

√75264 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75264 to simplify the square root of 75264. 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 75264. The factors of 75264 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 64, 84, 96, 98, 112, 128, 147, 168, 192, 196, 224, 256, 294, 336, 384, 392, 448, 512, 588, 672, 768, 784, 896, 1176, 1344, 1536, 1568, 1792, 2352, 2688, 3136, 3584, 4704, 5376, 6272, 9408, 10752, 12544, 18816, 25088, 37632, and 75264. Furthermore, the greatest perfect square on this list is 12544 and the square root of 12544 is 112. Therefore, A equals 112.

B = Calculate 75264 divided by the greatest perfect square from the list of all factors of 75264. We determined above that the greatest perfect square from the list of all factors of 75264 is 12544. Furthermore, 75264 divided by 12544 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 75264 in its simplest radical form as follows:

√75264 = A√B

√75264 = 112√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75264 to simplify the square root of 75264 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 75264 and then take the square root of that product. The prime factors that multiply together to make 75264 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7. 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 7 x 7 = 12544 and the square root of 12544 is 112. Therefore, A equals 112.

B = Divide 75264 by the number (A) squared. 112 squared is 12544 and 75264 divided by 12544 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 75264 in its simplest radical form as follows:

√75264 = A√B

√75264 = 112√6

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Simplify Square Root of 75265
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