Simplify Square Root of 50562

Here we will show you two methods that you can use to simplify the square root of 50562. In other words, we will show you how to find the square root of 50562 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.

√50562 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50562 to simplify the square root of 50562. 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 50562. The factors of 50562 are 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954, 2809, 5618, 8427, 16854, 25281, and 50562. Furthermore, the greatest perfect square on this list is 25281 and the square root of 25281 is 159. Therefore, A equals 159.

B = Calculate 50562 divided by the greatest perfect square from the list of all factors of 50562. We determined above that the greatest perfect square from the list of all factors of 50562 is 25281. Furthermore, 50562 divided by 25281 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 50562 in its simplest radical form as follows:

√50562 = A√B

√50562 = 159√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50562 to simplify the square root of 50562 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 50562 and then take the square root of that product. The prime factors that multiply together to make 50562 are 2 x 3 x 3 x 53 x 53. When we strip out the pairs only, we get 3 x 3 x 53 x 53 = 25281 and the square root of 25281 is 159. Therefore, A equals 159.

B = Divide 50562 by the number (A) squared. 159 squared is 25281 and 50562 divided by 25281 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 50562 in its simplest radical form as follows:

√50562 = A√B

√50562 = 159√2

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Simplify Square Root of 50563
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