Simplify Square Root of 51842

Here we will show you two methods that you can use to simplify the square root of 51842. In other words, we will show you how to find the square root of 51842 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.

√51842 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51842 to simplify the square root of 51842. 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 51842. The factors of 51842 are 1, 2, 7, 14, 23, 46, 49, 98, 161, 322, 529, 1058, 1127, 2254, 3703, 7406, 25921, and 51842. Furthermore, the greatest perfect square on this list is 25921 and the square root of 25921 is 161. Therefore, A equals 161.

B = Calculate 51842 divided by the greatest perfect square from the list of all factors of 51842. We determined above that the greatest perfect square from the list of all factors of 51842 is 25921. Furthermore, 51842 divided by 25921 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 51842 in its simplest radical form as follows:

√51842 = A√B

√51842 = 161√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51842 to simplify the square root of 51842 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 51842 and then take the square root of that product. The prime factors that multiply together to make 51842 are 2 x 7 x 7 x 23 x 23. When we strip out the pairs only, we get 7 x 7 x 23 x 23 = 25921 and the square root of 25921 is 161. Therefore, A equals 161.

B = Divide 51842 by the number (A) squared. 161 squared is 25921 and 51842 divided by 25921 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 51842 in its simplest radical form as follows:

√51842 = A√B

√51842 = 161√2

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Simplify Square Root of 51843
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