Simplify Square Root of 51304

Here we will show you two methods that you can use to simplify the square root of 51304. In other words, we will show you how to find the square root of 51304 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.

√51304 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51304 to simplify the square root of 51304. 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 51304. The factors of 51304 are 1, 2, 4, 8, 11, 22, 44, 53, 88, 106, 121, 212, 242, 424, 484, 583, 968, 1166, 2332, 4664, 6413, 12826, 25652, and 51304. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 51304 divided by the greatest perfect square from the list of all factors of 51304. We determined above that the greatest perfect square from the list of all factors of 51304 is 484. Furthermore, 51304 divided by 484 is 106, therefore B equals 106.

Now we have A and B and can get our answer to 51304 in its simplest radical form as follows:

√51304 = A√B

√51304 = 22√106

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51304 to simplify the square root of 51304 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 51304 and then take the square root of that product. The prime factors that multiply together to make 51304 are 2 x 2 x 2 x 11 x 11 x 53. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 51304 by the number (A) squared. 22 squared is 484 and 51304 divided by 484 is 106. Therefore, B equals 106.

Once again we have A and B and can get our answer to 51304 in its simplest radical form as follows:

√51304 = A√B

√51304 = 22√106

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Simplify Square Root of 51305
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