Simplify Square Root of 16562

Here we will show you two methods that you can use to simplify the square root of 16562. In other words, we will show you how to find the square root of 16562 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.

√16562 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 16562 to simplify the square root of 16562. 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 16562. The factors of 16562 are 1, 2, 7, 13, 14, 26, 49, 91, 98, 169, 182, 338, 637, 1183, 1274, 2366, 8281, and 16562. Furthermore, the greatest perfect square on this list is 8281 and the square root of 8281 is 91. Therefore, A equals 91.

B = Calculate 16562 divided by the greatest perfect square from the list of all factors of 16562. We determined above that the greatest perfect square from the list of all factors of 16562 is 8281. Furthermore, 16562 divided by 8281 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 16562 in its simplest radical form as follows:

√16562 = A√B

√16562 = 91√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 16562 to simplify the square root of 16562 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 16562 and then take the square root of that product. The prime factors that multiply together to make 16562 are 2 x 7 x 7 x 13 x 13. When we strip out the pairs only, we get 7 x 7 x 13 x 13 = 8281 and the square root of 8281 is 91. Therefore, A equals 91.

B = Divide 16562 by the number (A) squared. 91 squared is 8281 and 16562 divided by 8281 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 16562 in its simplest radical form as follows:

√16562 = A√B

√16562 = 91√2

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Simplify Square Root of 16563
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