Simplify Square Root of 19782

Here we will show you two methods that you can use to simplify the square root of 19782. In other words, we will show you how to find the square root of 19782 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.

√19782 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19782 to simplify the square root of 19782. 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 19782. The factors of 19782 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 157, 314, 471, 942, 1099, 1413, 2198, 2826, 3297, 6594, 9891, and 19782. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 19782 divided by the greatest perfect square from the list of all factors of 19782. We determined above that the greatest perfect square from the list of all factors of 19782 is 9. Furthermore, 19782 divided by 9 is 2198, therefore B equals 2198.

Now we have A and B and can get our answer to 19782 in its simplest radical form as follows:

√19782 = A√B

√19782 = 3√2198

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19782 to simplify the square root of 19782 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 19782 and then take the square root of that product. The prime factors that multiply together to make 19782 are 2 x 3 x 3 x 7 x 157. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 19782 by the number (A) squared. 3 squared is 9 and 19782 divided by 9 is 2198. Therefore, B equals 2198.

Once again we have A and B and can get our answer to 19782 in its simplest radical form as follows:

√19782 = A√B

√19782 = 3√2198

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Simplify Square Root of 19783
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