Simplify Square Root of 30225

Here we will show you two methods that you can use to simplify the square root of 30225. In other words, we will show you how to find the square root of 30225 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.

√30225 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30225 to simplify the square root of 30225. 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 30225. The factors of 30225 are 1, 3, 5, 13, 15, 25, 31, 39, 65, 75, 93, 155, 195, 325, 403, 465, 775, 975, 1209, 2015, 2325, 6045, 10075, and 30225. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 30225 divided by the greatest perfect square from the list of all factors of 30225. We determined above that the greatest perfect square from the list of all factors of 30225 is 25. Furthermore, 30225 divided by 25 is 1209, therefore B equals 1209.

Now we have A and B and can get our answer to 30225 in its simplest radical form as follows:

√30225 = A√B

√30225 = 5√1209

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30225 to simplify the square root of 30225 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 30225 and then take the square root of that product. The prime factors that multiply together to make 30225 are 3 x 5 x 5 x 13 x 31. 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 30225 by the number (A) squared. 5 squared is 25 and 30225 divided by 25 is 1209. Therefore, B equals 1209.

Once again we have A and B and can get our answer to 30225 in its simplest radical form as follows:

√30225 = A√B

√30225 = 5√1209

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Simplify Square Root of 30226
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