Simplify Square Root of 26752

Here we will show you two methods that you can use to simplify the square root of 26752. In other words, we will show you how to find the square root of 26752 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.

√26752 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26752 to simplify the square root of 26752. 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 26752. The factors of 26752 are 1, 2, 4, 8, 11, 16, 19, 22, 32, 38, 44, 64, 76, 88, 128, 152, 176, 209, 304, 352, 418, 608, 704, 836, 1216, 1408, 1672, 2432, 3344, 6688, 13376, and 26752. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 26752 divided by the greatest perfect square from the list of all factors of 26752. We determined above that the greatest perfect square from the list of all factors of 26752 is 64. Furthermore, 26752 divided by 64 is 418, therefore B equals 418.

Now we have A and B and can get our answer to 26752 in its simplest radical form as follows:

√26752 = A√B

√26752 = 8√418

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26752 to simplify the square root of 26752 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 26752 and then take the square root of that product. The prime factors that multiply together to make 26752 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 26752 by the number (A) squared. 8 squared is 64 and 26752 divided by 64 is 418. Therefore, B equals 418.

Once again we have A and B and can get our answer to 26752 in its simplest radical form as follows:

√26752 = A√B

√26752 = 8√418

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