Simplify Square Root of 25344

Here we will show you two methods that you can use to simplify the square root of 25344. In other words, we will show you how to find the square root of 25344 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.

√25344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25344 to simplify the square root of 25344. 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 25344. The factors of 25344 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 64, 66, 72, 88, 96, 99, 128, 132, 144, 176, 192, 198, 256, 264, 288, 352, 384, 396, 528, 576, 704, 768, 792, 1056, 1152, 1408, 1584, 2112, 2304, 2816, 3168, 4224, 6336, 8448, 12672, and 25344. Furthermore, the greatest perfect square on this list is 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Calculate 25344 divided by the greatest perfect square from the list of all factors of 25344. We determined above that the greatest perfect square from the list of all factors of 25344 is 2304. Furthermore, 25344 divided by 2304 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 25344 in its simplest radical form as follows:

√25344 = A√B

√25344 = 48√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25344 to simplify the square root of 25344 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 25344 and then take the square root of that product. The prime factors that multiply together to make 25344 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11. 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 3 x 3 = 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Divide 25344 by the number (A) squared. 48 squared is 2304 and 25344 divided by 2304 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 25344 in its simplest radical form as follows:

√25344 = A√B

√25344 = 48√11

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Simplify Square Root of 25345
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