# Thread: Sum of cubic roots yields an integer

1. Determine the positive numbers, $a$, such that the sum:

$$\sqrt[3]{3+\sqrt{a}}+\sqrt[3]{3-\sqrt{a}}$$

is an integer.

2. Originally Posted by lfdahl
Determine the positive numbers, $a$, such that the sum:

$$\sqrt[3]{3+\sqrt{a}}+\sqrt[3]{3-\sqrt{a}}$$

is an integer.
my solution:

Originally Posted by Albert

4. Originally Posted by lfdahl
another solution:

Originally Posted by Albert
Well done, thankyou Albert!

An alternative approach can be found here: