Simplify Square Root of 18513

Here we will show you two methods that you can use to simplify the square root of 18513. In other words, we will show you how to find the square root of 18513 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.

√18513 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18513 to simplify the square root of 18513. 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 18513. The factors of 18513 are 1, 3, 9, 11, 17, 33, 51, 99, 121, 153, 187, 363, 561, 1089, 1683, 2057, 6171, and 18513. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 18513 divided by the greatest perfect square from the list of all factors of 18513. We determined above that the greatest perfect square from the list of all factors of 18513 is 1089. Furthermore, 18513 divided by 1089 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 18513 in its simplest radical form as follows:

√18513 = A√B

√18513 = 33√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18513 to simplify the square root of 18513 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 18513 and then take the square root of that product. The prime factors that multiply together to make 18513 are 3 x 3 x 11 x 11 x 17. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 18513 by the number (A) squared. 33 squared is 1089 and 18513 divided by 1089 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 18513 in its simplest radical form as follows:

√18513 = A√B

√18513 = 33√17

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Simplify Square Root of 18514
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