Simplify Square Root of 77618

Here we will show you two methods that you can use to simplify the square root of 77618. In other words, we will show you how to find the square root of 77618 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.

√77618 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77618 to simplify the square root of 77618. 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 77618. The factors of 77618 are 1, 2, 197, 394, 38809, and 77618. Furthermore, the greatest perfect square on this list is 38809 and the square root of 38809 is 197. Therefore, A equals 197.

B = Calculate 77618 divided by the greatest perfect square from the list of all factors of 77618. We determined above that the greatest perfect square from the list of all factors of 77618 is 38809. Furthermore, 77618 divided by 38809 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 77618 in its simplest radical form as follows:

√77618 = A√B

√77618 = 197√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77618 to simplify the square root of 77618 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 77618 and then take the square root of that product. The prime factors that multiply together to make 77618 are 2 x 197 x 197. When we strip out the pairs only, we get 197 x 197 = 38809 and the square root of 38809 is 197. Therefore, A equals 197.

B = Divide 77618 by the number (A) squared. 197 squared is 38809 and 77618 divided by 38809 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 77618 in its simplest radical form as follows:

√77618 = A√B

√77618 = 197√2

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Simplify Square Root of 77619
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