Simplify Square Root of 9225

Here we will show you two methods that you can use to simplify the square root of 9225. In other words, we will show you how to find the square root of 9225 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.

√9225 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9225 to simplify the square root of 9225. 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 9225. The factors of 9225 are 1, 3, 5, 9, 15, 25, 41, 45, 75, 123, 205, 225, 369, 615, 1025, 1845, 3075, and 9225. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 9225 divided by the greatest perfect square from the list of all factors of 9225. We determined above that the greatest perfect square from the list of all factors of 9225 is 225. Furthermore, 9225 divided by 225 is 41, therefore B equals 41.

Now we have A and B and can get our answer to 9225 in its simplest radical form as follows:

√9225 = A√B

√9225 = 15√41

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9225 to simplify the square root of 9225 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 9225 and then take the square root of that product. The prime factors that multiply together to make 9225 are 3 x 3 x 5 x 5 x 41. 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 9225 by the number (A) squared. 15 squared is 225 and 9225 divided by 225 is 41. Therefore, B equals 41.

Once again we have A and B and can get our answer to 9225 in its simplest radical form as follows:

√9225 = A√B

√9225 = 15√41

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Simplify Square Root of 9226
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