Simplify Square Root of 57834

Here we will show you two methods that you can use to simplify the square root of 57834. In other words, we will show you how to find the square root of 57834 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.

√57834 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57834 to simplify the square root of 57834. 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 57834. The factors of 57834 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 27, 34, 42, 51, 54, 63, 81, 102, 119, 126, 153, 162, 189, 238, 243, 306, 357, 378, 459, 486, 567, 714, 918, 1071, 1134, 1377, 1701, 2142, 2754, 3213, 3402, 4131, 6426, 8262, 9639, 19278, 28917, and 57834. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 57834 divided by the greatest perfect square from the list of all factors of 57834. We determined above that the greatest perfect square from the list of all factors of 57834 is 81. Furthermore, 57834 divided by 81 is 714, therefore B equals 714.

Now we have A and B and can get our answer to 57834 in its simplest radical form as follows:

√57834 = A√B

√57834 = 9√714

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57834 to simplify the square root of 57834 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 57834 and then take the square root of that product. The prime factors that multiply together to make 57834 are 2 x 3 x 3 x 3 x 3 x 3 x 7 x 17. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 57834 by the number (A) squared. 9 squared is 81 and 57834 divided by 81 is 714. Therefore, B equals 714.

Once again we have A and B and can get our answer to 57834 in its simplest radical form as follows:

√57834 = A√B

√57834 = 9√714

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