Simplify Square Root of 5050

Here we will show you two methods that you can use to simplify the square root of 5050. In other words, we will show you how to find the square root of 5050 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.

√5050 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5050 to simplify the square root of 5050. 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 5050. The factors of 5050 are 1, 2, 5, 10, 25, 50, 101, 202, 505, 1010, 2525, and 5050. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 5050 divided by the greatest perfect square from the list of all factors of 5050. We determined above that the greatest perfect square from the list of all factors of 5050 is 25. Furthermore, 5050 divided by 25 is 202, therefore B equals 202.

Now we have A and B and can get our answer to 5050 in its simplest radical form as follows:

√5050 = A√B

√5050 = 5√202

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5050 to simplify the square root of 5050 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 5050 and then take the square root of that product. The prime factors that multiply together to make 5050 are 2 x 5 x 5 x 101. 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 5050 by the number (A) squared. 5 squared is 25 and 5050 divided by 25 is 202. Therefore, B equals 202.

Once again we have A and B and can get our answer to 5050 in its simplest radical form as follows:

√5050 = A√B

√5050 = 5√202

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Simplify Square Root of 5051
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