Simplify Square Root of 49700

Here we will show you two methods that you can use to simplify the square root of 49700. In other words, we will show you how to find the square root of 49700 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.

√49700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49700 to simplify the square root of 49700. 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 49700. The factors of 49700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 71, 100, 140, 142, 175, 284, 350, 355, 497, 700, 710, 994, 1420, 1775, 1988, 2485, 3550, 4970, 7100, 9940, 12425, 24850, and 49700. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 49700 divided by the greatest perfect square from the list of all factors of 49700. We determined above that the greatest perfect square from the list of all factors of 49700 is 100. Furthermore, 49700 divided by 100 is 497, therefore B equals 497.

Now we have A and B and can get our answer to 49700 in its simplest radical form as follows:

√49700 = A√B

√49700 = 10√497

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49700 to simplify the square root of 49700 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 49700 and then take the square root of that product. The prime factors that multiply together to make 49700 are 2 x 2 x 5 x 5 x 7 x 71. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 49700 by the number (A) squared. 10 squared is 100 and 49700 divided by 100 is 497. Therefore, B equals 497.

Once again we have A and B and can get our answer to 49700 in its simplest radical form as follows:

√49700 = A√B

√49700 = 10√497

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