Simplify Square Root of 19350

Here we will show you two methods that you can use to simplify the square root of 19350. In other words, we will show you how to find the square root of 19350 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.

√19350 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19350 to simplify the square root of 19350. 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 19350. The factors of 19350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 43, 45, 50, 75, 86, 90, 129, 150, 215, 225, 258, 387, 430, 450, 645, 774, 1075, 1290, 1935, 2150, 3225, 3870, 6450, 9675, and 19350. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 19350 divided by the greatest perfect square from the list of all factors of 19350. We determined above that the greatest perfect square from the list of all factors of 19350 is 225. Furthermore, 19350 divided by 225 is 86, therefore B equals 86.

Now we have A and B and can get our answer to 19350 in its simplest radical form as follows:

√19350 = A√B

√19350 = 15√86

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19350 to simplify the square root of 19350 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 19350 and then take the square root of that product. The prime factors that multiply together to make 19350 are 2 x 3 x 3 x 5 x 5 x 43. 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 19350 by the number (A) squared. 15 squared is 225 and 19350 divided by 225 is 86. Therefore, B equals 86.

Once again we have A and B and can get our answer to 19350 in its simplest radical form as follows:

√19350 = A√B

√19350 = 15√86

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