Simplify Square Root of 19425

Here we will show you two methods that you can use to simplify the square root of 19425. In other words, we will show you how to find the square root of 19425 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.

√19425 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19425 to simplify the square root of 19425. 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 19425. The factors of 19425 are 1, 3, 5, 7, 15, 21, 25, 35, 37, 75, 105, 111, 175, 185, 259, 525, 555, 777, 925, 1295, 2775, 3885, 6475, and 19425. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 19425 divided by the greatest perfect square from the list of all factors of 19425. We determined above that the greatest perfect square from the list of all factors of 19425 is 25. Furthermore, 19425 divided by 25 is 777, therefore B equals 777.

Now we have A and B and can get our answer to 19425 in its simplest radical form as follows:

√19425 = A√B

√19425 = 5√777

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19425 to simplify the square root of 19425 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 19425 and then take the square root of that product. The prime factors that multiply together to make 19425 are 3 x 5 x 5 x 7 x 37. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 19425 by the number (A) squared. 5 squared is 25 and 19425 divided by 25 is 777. Therefore, B equals 777.

Once again we have A and B and can get our answer to 19425 in its simplest radical form as follows:

√19425 = A√B

√19425 = 5√777

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Simplify Square Root of 19426
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