Simplify Square Root of 49298

Here we will show you two methods that you can use to simplify the square root of 49298. In other words, we will show you how to find the square root of 49298 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.

√49298 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49298 to simplify the square root of 49298. 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 49298. The factors of 49298 are 1, 2, 157, 314, 24649, and 49298. Furthermore, the greatest perfect square on this list is 24649 and the square root of 24649 is 157. Therefore, A equals 157.

B = Calculate 49298 divided by the greatest perfect square from the list of all factors of 49298. We determined above that the greatest perfect square from the list of all factors of 49298 is 24649. Furthermore, 49298 divided by 24649 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 49298 in its simplest radical form as follows:

√49298 = A√B

√49298 = 157√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49298 to simplify the square root of 49298 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 49298 and then take the square root of that product. The prime factors that multiply together to make 49298 are 2 x 157 x 157. When we strip out the pairs only, we get 157 x 157 = 24649 and the square root of 24649 is 157. Therefore, A equals 157.

B = Divide 49298 by the number (A) squared. 157 squared is 24649 and 49298 divided by 24649 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 49298 in its simplest radical form as follows:

√49298 = A√B

√49298 = 157√2

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