Simplify Square Root of 65050

Here we will show you two methods that you can use to simplify the square root of 65050. In other words, we will show you how to find the square root of 65050 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.

√65050 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65050 to simplify the square root of 65050. 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 65050. The factors of 65050 are 1, 2, 5, 10, 25, 50, 1301, 2602, 6505, 13010, 32525, and 65050. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 65050 divided by the greatest perfect square from the list of all factors of 65050. We determined above that the greatest perfect square from the list of all factors of 65050 is 25. Furthermore, 65050 divided by 25 is 2602, therefore B equals 2602.

Now we have A and B and can get our answer to 65050 in its simplest radical form as follows:

√65050 = A√B

√65050 = 5√2602

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65050 to simplify the square root of 65050 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 65050 and then take the square root of that product. The prime factors that multiply together to make 65050 are 2 x 5 x 5 x 1301. 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 65050 by the number (A) squared. 5 squared is 25 and 65050 divided by 25 is 2602. Therefore, B equals 2602.

Once again we have A and B and can get our answer to 65050 in its simplest radical form as follows:

√65050 = A√B

√65050 = 5√2602

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Simplify Square Root of 65051
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