Simplify. Assume c is nonnegative.

radical over 16c^19 = 


To simplify the expression \(\sqrt{16c^{19}}\), follow these steps:

1. **Separate the square root**: Break it down into the product of square roots:

\[
\sqrt{16c^{19}} = \sqrt{16} \times \sqrt{c^{19}}
\]

2. **Simplify the square root of 16**: 

\[
\sqrt{16} = 4
\]

3. **Simplify the square root of \(c^{19}\)**: 

\[
\sqrt{c^{19}} = c^{\frac{19}{2}} = c^9 \times \sqrt{c}
\]

So, putting it all together:

\[
\sqrt{16c^{19}} = 4c^9 \times \sqrt{c}
\]

The simplified expression is:

\[
4c^9 \sqrt{c}
\]

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you simplify \(\sqrt{25c^{10}}\)?
2. What is the simplified form of \(\sqrt{9c^{14}}\)?
3. How do you simplify expressions with fractional exponents?
4. What is the square root of a negative number?
5. How do you simplify \(\sqrt{64c^{20}}\)?

**Tip:** When simplifying square roots with variables, remember to split the exponent into an even part and an odd part to make the simplification easier.

Learn how to simplify the expression √(16c^19) step-by-step. This problem involves square roots and exponents, specifically focusing on simplification techniques. Suitable for Grades 9-12 students and anyone interested in algebraic simplification.

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