Simplify Square Root of 33462

Here we will show you two methods that you can use to simplify the square root of 33462. In other words, we will show you how to find the square root of 33462 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.

√33462 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33462 to simplify the square root of 33462. 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 33462. The factors of 33462 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 169, 198, 234, 286, 338, 429, 507, 858, 1014, 1287, 1521, 1859, 2574, 3042, 3718, 5577, 11154, 16731, and 33462. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 33462 divided by the greatest perfect square from the list of all factors of 33462. We determined above that the greatest perfect square from the list of all factors of 33462 is 1521. Furthermore, 33462 divided by 1521 is 22, therefore B equals 22.

Now we have A and B and can get our answer to 33462 in its simplest radical form as follows:

√33462 = A√B

√33462 = 39√22

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33462 to simplify the square root of 33462 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 33462 and then take the square root of that product. The prime factors that multiply together to make 33462 are 2 x 3 x 3 x 11 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 33462 by the number (A) squared. 39 squared is 1521 and 33462 divided by 1521 is 22. Therefore, B equals 22.

Once again we have A and B and can get our answer to 33462 in its simplest radical form as follows:

√33462 = A√B

√33462 = 39√22

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