Let's break down the expression $\sqrt{9x^{10}}$:

Step 1: Simplify the square root of the constant.

$\sqrt{9} = 3$

Step 2: Simplify the square root of $x^{10}$.

When taking the square root of $x^{10}$, you are effectively dividing the exponent by 2: $\sqrt{x^{10}} = x^{10/2} = x^5$

Step 3: Combine the results.

So, the simplified form is: $\sqrt{9x^{10}} = 3x^5$

This matches the answer choice: $3x^5$

Answer:

The correct answer is: $3x^5$

Would you like more details or have any other questions?

Here are 5 related questions for practice:

1. Simplify $\sqrt{16x^{8}}$.
2. Simplify $\sqrt{25x^{12}}$.
3. Express $\sqrt{4x^{14}}$ in simplest form.
4. What is $\sqrt{36y^6}$?
5. Simplify $\sqrt{49x^{16}}$.

Tip: When simplifying square roots involving exponents, always divide the exponent by 2. If the exponent is odd, separate the variable into two parts: one that has an even exponent and one that does not.