Simplify Square Root of 69459

Here we will show you two methods that you can use to simplify the square root of 69459. In other words, we will show you how to find the square root of 69459 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.

√69459 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69459 to simplify the square root of 69459. 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 69459. The factors of 69459 are 1, 3, 13, 39, 137, 169, 411, 507, 1781, 5343, 23153, and 69459. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 69459 divided by the greatest perfect square from the list of all factors of 69459. We determined above that the greatest perfect square from the list of all factors of 69459 is 169. Furthermore, 69459 divided by 169 is 411, therefore B equals 411.

Now we have A and B and can get our answer to 69459 in its simplest radical form as follows:

√69459 = A√B

√69459 = 13√411

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69459 to simplify the square root of 69459 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 69459 and then take the square root of that product. The prime factors that multiply together to make 69459 are 3 x 13 x 13 x 137. 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 69459 by the number (A) squared. 13 squared is 169 and 69459 divided by 169 is 411. Therefore, B equals 411.

Once again we have A and B and can get our answer to 69459 in its simplest radical form as follows:

√69459 = A√B

√69459 = 13√411

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