Simplify Square Root of 30550

Here we will show you two methods that you can use to simplify the square root of 30550. In other words, we will show you how to find the square root of 30550 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.

√30550 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30550 to simplify the square root of 30550. 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 30550. The factors of 30550 are 1, 2, 5, 10, 13, 25, 26, 47, 50, 65, 94, 130, 235, 325, 470, 611, 650, 1175, 1222, 2350, 3055, 6110, 15275, and 30550. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 30550 divided by the greatest perfect square from the list of all factors of 30550. We determined above that the greatest perfect square from the list of all factors of 30550 is 25. Furthermore, 30550 divided by 25 is 1222, therefore B equals 1222.

Now we have A and B and can get our answer to 30550 in its simplest radical form as follows:

√30550 = A√B

√30550 = 5√1222

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30550 to simplify the square root of 30550 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 30550 and then take the square root of that product. The prime factors that multiply together to make 30550 are 2 x 5 x 5 x 13 x 47. 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 30550 by the number (A) squared. 5 squared is 25 and 30550 divided by 25 is 1222. Therefore, B equals 1222.

Once again we have A and B and can get our answer to 30550 in its simplest radical form as follows:

√30550 = A√B

√30550 = 5√1222

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Simplify Square Root of 30551
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