The expression in the image is:

$\sqrt{49u^9}$

We are asked to simplify this expression, assuming $u$ is a positive real number.

Steps for simplification:

1. Simplify the square root of 49: $\sqrt{49} = 7$

2. Simplify the square root of $u^9$: Using the property of square roots: $\sqrt{u^9} = u^{\frac{9}{2}} = u^4 \cdot u^{\frac{1}{2}} = u^4 \sqrt{u}$

3. Combine the results: $\sqrt{49u^9} = 7u^4 \sqrt{u}$

Thus, the simplified expression is:

$7u^4 \sqrt{u}$

Would you like more details or have any other questions?

Here are five related questions to expand your understanding:

1. How would you simplify $\sqrt{81x^6}$?
2. What happens if the exponent of $u$ was an even number in the original expression?
3. How do you simplify cube roots for expressions with variables?
4. What are the key rules for handling exponents under radicals?
5. How would the simplification change if $u$ were not a positive real number?

Tip: When simplifying square roots of variables, remember to check if the exponents are odd or even. This helps you split the variable into parts that can be simplified more easily!