Simplify Square Root of 10025

Here we will show you two methods that you can use to simplify the square root of 10025. In other words, we will show you how to find the square root of 10025 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.

√10025 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10025 to simplify the square root of 10025. 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 10025. The factors of 10025 are 1, 5, 25, 401, 2005, and 10025. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 10025 divided by the greatest perfect square from the list of all factors of 10025. We determined above that the greatest perfect square from the list of all factors of 10025 is 25. Furthermore, 10025 divided by 25 is 401, therefore B equals 401.

Now we have A and B and can get our answer to 10025 in its simplest radical form as follows:

√10025 = A√B

√10025 = 5√401

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10025 to simplify the square root of 10025 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 10025 and then take the square root of that product. The prime factors that multiply together to make 10025 are 5 x 5 x 401. 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 10025 by the number (A) squared. 5 squared is 25 and 10025 divided by 25 is 401. Therefore, B equals 401.

Once again we have A and B and can get our answer to 10025 in its simplest radical form as follows:

√10025 = A√B

√10025 = 5√401

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Simplify Square Root of 10026
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