Simplify Square Root of 26352

Here we will show you two methods that you can use to simplify the square root of 26352. In other words, we will show you how to find the square root of 26352 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.

√26352 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26352 to simplify the square root of 26352. 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 26352. The factors of 26352 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 61, 72, 108, 122, 144, 183, 216, 244, 366, 432, 488, 549, 732, 976, 1098, 1464, 1647, 2196, 2928, 3294, 4392, 6588, 8784, 13176, and 26352. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 26352 divided by the greatest perfect square from the list of all factors of 26352. We determined above that the greatest perfect square from the list of all factors of 26352 is 144. Furthermore, 26352 divided by 144 is 183, therefore B equals 183.

Now we have A and B and can get our answer to 26352 in its simplest radical form as follows:

√26352 = A√B

√26352 = 12√183

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26352 to simplify the square root of 26352 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 26352 and then take the square root of that product. The prime factors that multiply together to make 26352 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 61. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 26352 by the number (A) squared. 12 squared is 144 and 26352 divided by 144 is 183. Therefore, B equals 183.

Once again we have A and B and can get our answer to 26352 in its simplest radical form as follows:

√26352 = A√B

√26352 = 12√183

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