Simplify Square Root of 55738

Here we will show you two methods that you can use to simplify the square root of 55738. In other words, we will show you how to find the square root of 55738 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.

√55738 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55738 to simplify the square root of 55738. 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 55738. The factors of 55738 are 1, 2, 29, 31, 58, 62, 899, 961, 1798, 1922, 27869, and 55738. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 55738 divided by the greatest perfect square from the list of all factors of 55738. We determined above that the greatest perfect square from the list of all factors of 55738 is 961. Furthermore, 55738 divided by 961 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 55738 in its simplest radical form as follows:

√55738 = A√B

√55738 = 31√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55738 to simplify the square root of 55738 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 55738 and then take the square root of that product. The prime factors that multiply together to make 55738 are 2 x 29 x 31 x 31. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 55738 by the number (A) squared. 31 squared is 961 and 55738 divided by 961 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 55738 in its simplest radical form as follows:

√55738 = A√B

√55738 = 31√58

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Simplify Square Root of 55739
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