Simplify Square Root of 63749

Here we will show you two methods that you can use to simplify the square root of 63749. In other words, we will show you how to find the square root of 63749 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.

√63749 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63749 to simplify the square root of 63749. 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 63749. The factors of 63749 are 1, 7, 49, 1301, 9107, and 63749. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 63749 divided by the greatest perfect square from the list of all factors of 63749. We determined above that the greatest perfect square from the list of all factors of 63749 is 49. Furthermore, 63749 divided by 49 is 1301, therefore B equals 1301.

Now we have A and B and can get our answer to 63749 in its simplest radical form as follows:

√63749 = A√B

√63749 = 7√1301

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63749 to simplify the square root of 63749 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 63749 and then take the square root of that product. The prime factors that multiply together to make 63749 are 7 x 7 x 1301. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 63749 by the number (A) squared. 7 squared is 49 and 63749 divided by 49 is 1301. Therefore, B equals 1301.

Once again we have A and B and can get our answer to 63749 in its simplest radical form as follows:

√63749 = A√B

√63749 = 7√1301

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