Simplify Square Root of 55778

Here we will show you two methods that you can use to simplify the square root of 55778. In other words, we will show you how to find the square root of 55778 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.

√55778 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55778 to simplify the square root of 55778. 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 55778. The factors of 55778 are 1, 2, 167, 334, 27889, and 55778. Furthermore, the greatest perfect square on this list is 27889 and the square root of 27889 is 167. Therefore, A equals 167.

B = Calculate 55778 divided by the greatest perfect square from the list of all factors of 55778. We determined above that the greatest perfect square from the list of all factors of 55778 is 27889. Furthermore, 55778 divided by 27889 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 55778 in its simplest radical form as follows:

√55778 = A√B

√55778 = 167√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55778 to simplify the square root of 55778 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 55778 and then take the square root of that product. The prime factors that multiply together to make 55778 are 2 x 167 x 167. When we strip out the pairs only, we get 167 x 167 = 27889 and the square root of 27889 is 167. Therefore, A equals 167.

B = Divide 55778 by the number (A) squared. 167 squared is 27889 and 55778 divided by 27889 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 55778 in its simplest radical form as follows:

√55778 = A√B

√55778 = 167√2

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Simplify Square Root of 55779
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