Simplify Square Root of 825

Here we will show you two methods that you can use to simplify the square root of 825. In other words, we will show you how to find the square root of 825 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.

√825 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 825 to simplify the square root of 825. 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 825. The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 825 divided by the greatest perfect square from the list of all factors of 825. We determined above that the greatest perfect square from the list of all factors of 825 is 25. Furthermore, 825 divided by 25 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 825 in its simplest radical form as follows:

√825 = A√B

√825 = 5√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 825 to simplify the square root of 825 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 825 and then take the square root of that product. The prime factors that multiply together to make 825 are 3 x 5 x 5 x 11. 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 825 by the number (A) squared. 5 squared is 25 and 825 divided by 25 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 825 in its simplest radical form as follows:

√825 = A√B

√825 = 5√33

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Simplify Square Root of 826
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