When you encounter a square root inside of a square root, you’re dealing with a nested radical expression. The key to simplifying such expressions is to carefully break them down step by step.
For instance, consider the expression √(√x). To simplify, you can rewrite it as x raised to the power of 1/4. This is because the square root of a number can be expressed as that number to the power of 1/2, and when you take the square root again, you multiply the exponents: (1/2) * (1/2) = 1/4.
Another approach is to try to simplify the innermost square root first. If you have an expression like √(√(x^2 + 4)), you would first simplify the inner square root and then address the outer one. In simpler terms, you can think of it as peeling back the layers of an onion, handling each radical one at a time.
If further simplification isn’t possible or you’re dealing with a more complex expression, you might also consider leaving the expression in its original nested form, as it can sometimes be more manageable that way. Just remember: breaking things down step by step often reveals a clearer path to the solution.