Simplify Square Root of 51750

Here we will show you two methods that you can use to simplify the square root of 51750. In other words, we will show you how to find the square root of 51750 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.

√51750 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51750 to simplify the square root of 51750. 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 51750. The factors of 51750 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 25, 30, 45, 46, 50, 69, 75, 90, 115, 125, 138, 150, 207, 225, 230, 250, 345, 375, 414, 450, 575, 690, 750, 1035, 1125, 1150, 1725, 2070, 2250, 2875, 3450, 5175, 5750, 8625, 10350, 17250, 25875, and 51750. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 51750 divided by the greatest perfect square from the list of all factors of 51750. We determined above that the greatest perfect square from the list of all factors of 51750 is 225. Furthermore, 51750 divided by 225 is 230, therefore B equals 230.

Now we have A and B and can get our answer to 51750 in its simplest radical form as follows:

√51750 = A√B

√51750 = 15√230

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51750 to simplify the square root of 51750 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 51750 and then take the square root of that product. The prime factors that multiply together to make 51750 are 2 x 3 x 3 x 5 x 5 x 5 x 23. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 51750 by the number (A) squared. 15 squared is 225 and 51750 divided by 225 is 230. Therefore, B equals 230.

Once again we have A and B and can get our answer to 51750 in its simplest radical form as follows:

√51750 = A√B

√51750 = 15√230

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