Simplify Square Root of 51300

Here we will show you two methods that you can use to simplify the square root of 51300. In other words, we will show you how to find the square root of 51300 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.

√51300 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51300 to simplify the square root of 51300. 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 51300. The factors of 51300 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 27, 30, 36, 38, 45, 50, 54, 57, 60, 75, 76, 90, 95, 100, 108, 114, 135, 150, 171, 180, 190, 225, 228, 270, 285, 300, 342, 380, 450, 475, 513, 540, 570, 675, 684, 855, 900, 950, 1026, 1140, 1350, 1425, 1710, 1900, 2052, 2565, 2700, 2850, 3420, 4275, 5130, 5700, 8550, 10260, 12825, 17100, 25650, and 51300. Furthermore, the greatest perfect square on this list is 900 and the square root of 900 is 30. Therefore, A equals 30.

B = Calculate 51300 divided by the greatest perfect square from the list of all factors of 51300. We determined above that the greatest perfect square from the list of all factors of 51300 is 900. Furthermore, 51300 divided by 900 is 57, therefore B equals 57.

Now we have A and B and can get our answer to 51300 in its simplest radical form as follows:

√51300 = A√B

√51300 = 30√57

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51300 to simplify the square root of 51300 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 51300 and then take the square root of that product. The prime factors that multiply together to make 51300 are 2 x 2 x 3 x 3 x 3 x 5 x 5 x 19. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 5 x 5 = 900 and the square root of 900 is 30. Therefore, A equals 30.

B = Divide 51300 by the number (A) squared. 30 squared is 900 and 51300 divided by 900 is 57. Therefore, B equals 57.

Once again we have A and B and can get our answer to 51300 in its simplest radical form as follows:

√51300 = A√B

√51300 = 30√57

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