Simplify Square Root of 49525

Here we will show you two methods that you can use to simplify the square root of 49525. In other words, we will show you how to find the square root of 49525 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.

√49525 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49525 to simplify the square root of 49525. 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 49525. The factors of 49525 are 1, 5, 7, 25, 35, 175, 283, 1415, 1981, 7075, 9905, and 49525. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 49525 divided by the greatest perfect square from the list of all factors of 49525. We determined above that the greatest perfect square from the list of all factors of 49525 is 25. Furthermore, 49525 divided by 25 is 1981, therefore B equals 1981.

Now we have A and B and can get our answer to 49525 in its simplest radical form as follows:

√49525 = A√B

√49525 = 5√1981

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49525 to simplify the square root of 49525 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 49525 and then take the square root of that product. The prime factors that multiply together to make 49525 are 5 x 5 x 7 x 283. 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 49525 by the number (A) squared. 5 squared is 25 and 49525 divided by 25 is 1981. Therefore, B equals 1981.

Once again we have A and B and can get our answer to 49525 in its simplest radical form as follows:

√49525 = A√B

√49525 = 5√1981

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Simplify Square Root of 49526
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