Simplify Square Root of 9495

Here we will show you two methods that you can use to simplify the square root of 9495. In other words, we will show you how to find the square root of 9495 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.

√9495 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9495 to simplify the square root of 9495. 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 9495. The factors of 9495 are 1, 3, 5, 9, 15, 45, 211, 633, 1055, 1899, 3165, and 9495. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 9495 divided by the greatest perfect square from the list of all factors of 9495. We determined above that the greatest perfect square from the list of all factors of 9495 is 9. Furthermore, 9495 divided by 9 is 1055, therefore B equals 1055.

Now we have A and B and can get our answer to 9495 in its simplest radical form as follows:

√9495 = A√B

√9495 = 3√1055

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9495 to simplify the square root of 9495 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 9495 and then take the square root of that product. The prime factors that multiply together to make 9495 are 3 x 3 x 5 x 211. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 9495 by the number (A) squared. 3 squared is 9 and 9495 divided by 9 is 1055. Therefore, B equals 1055.

Once again we have A and B and can get our answer to 9495 in its simplest radical form as follows:

√9495 = A√B

√9495 = 3√1055

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