Simplify Square Root of 51524

Here we will show you two methods that you can use to simplify the square root of 51524. In other words, we will show you how to find the square root of 51524 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.

√51524 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51524 to simplify the square root of 51524. 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 51524. The factors of 51524 are 1, 2, 4, 11, 22, 44, 1171, 2342, 4684, 12881, 25762, and 51524. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 51524 divided by the greatest perfect square from the list of all factors of 51524. We determined above that the greatest perfect square from the list of all factors of 51524 is 4. Furthermore, 51524 divided by 4 is 12881, therefore B equals 12881.

Now we have A and B and can get our answer to 51524 in its simplest radical form as follows:

√51524 = A√B

√51524 = 2√12881

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51524 to simplify the square root of 51524 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 51524 and then take the square root of that product. The prime factors that multiply together to make 51524 are 2 x 2 x 11 x 1171. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 51524 by the number (A) squared. 2 squared is 4 and 51524 divided by 4 is 12881. Therefore, B equals 12881.

Once again we have A and B and can get our answer to 51524 in its simplest radical form as follows:

√51524 = A√B

√51524 = 2√12881

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