Simplify Square Root of 10625

Here we will show you two methods that you can use to simplify the square root of 10625. In other words, we will show you how to find the square root of 10625 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.

√10625 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10625 to simplify the square root of 10625. 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 10625. The factors of 10625 are 1, 5, 17, 25, 85, 125, 425, 625, 2125, and 10625. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 10625 divided by the greatest perfect square from the list of all factors of 10625. We determined above that the greatest perfect square from the list of all factors of 10625 is 625. Furthermore, 10625 divided by 625 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 10625 in its simplest radical form as follows:

√10625 = A√B

√10625 = 25√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10625 to simplify the square root of 10625 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 10625 and then take the square root of that product. The prime factors that multiply together to make 10625 are 5 x 5 x 5 x 5 x 17. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 10625 by the number (A) squared. 25 squared is 625 and 10625 divided by 625 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 10625 in its simplest radical form as follows:

√10625 = A√B

√10625 = 25√17

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Simplify Square Root of 10626
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