Simplify Square Root of 70785

Here we will show you two methods that you can use to simplify the square root of 70785. In other words, we will show you how to find the square root of 70785 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.

√70785 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70785 to simplify the square root of 70785. 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 70785. The factors of 70785 are 1, 3, 5, 9, 11, 13, 15, 33, 39, 45, 55, 65, 99, 117, 121, 143, 165, 195, 363, 429, 495, 585, 605, 715, 1089, 1287, 1573, 1815, 2145, 4719, 5445, 6435, 7865, 14157, 23595, and 70785. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 70785 divided by the greatest perfect square from the list of all factors of 70785. We determined above that the greatest perfect square from the list of all factors of 70785 is 1089. Furthermore, 70785 divided by 1089 is 65, therefore B equals 65.

Now we have A and B and can get our answer to 70785 in its simplest radical form as follows:

√70785 = A√B

√70785 = 33√65

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70785 to simplify the square root of 70785 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 70785 and then take the square root of that product. The prime factors that multiply together to make 70785 are 3 x 3 x 5 x 11 x 11 x 13. 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 70785 by the number (A) squared. 33 squared is 1089 and 70785 divided by 1089 is 65. Therefore, B equals 65.

Once again we have A and B and can get our answer to 70785 in its simplest radical form as follows:

√70785 = A√B

√70785 = 33√65

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