Simplify Square Root of 1859

Here we will show you two methods that you can use to simplify the square root of 1859. In other words, we will show you how to find the square root of 1859 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.

√1859 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 1859 to simplify the square root of 1859. 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 1859. The factors of 1859 are 1, 11, 13, 143, 169, and 1859. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 1859 divided by the greatest perfect square from the list of all factors of 1859. We determined above that the greatest perfect square from the list of all factors of 1859 is 169. Furthermore, 1859 divided by 169 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 1859 in its simplest radical form as follows:

√1859 = A√B

√1859 = 13√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 1859 to simplify the square root of 1859 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 1859 and then take the square root of that product. The prime factors that multiply together to make 1859 are 11 x 13 x 13. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 1859 by the number (A) squared. 13 squared is 169 and 1859 divided by 169 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 1859 in its simplest radical form as follows:

√1859 = A√B

√1859 = 13√11

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