We are given the expression $\sqrt{16x^8}$ and asked to simplify it using radical properties.

Step 1: Break the square root into two parts.

We can use the property of square roots that states: $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ So, we can rewrite the given expression as: $\sqrt{16x^8} = \sqrt{16} \cdot \sqrt{x^8}$

Step 2: Simplify each part.

• $\sqrt{16} = 4$, because $4^2 = 16$.
• For $\sqrt{x^8}$, we apply the rule $\sqrt{x^n} = x^{n/2}$. Thus: $\sqrt{x^8} = x^{8/2} = x^4$

Step 3: Combine the results.

Now, putting the two parts together: $\sqrt{16x^8} = 4 \cdot x^4$

Thus, the simplified form of $\sqrt{16x^8}$ is: $4x^4$

Would you like more details on radical properties or have any other questions?

5 Related Questions:

1. How do you simplify higher-order radicals like $\sqrt[3]{27x^6}$?
2. What are the key properties of radicals and exponents?
3. How can you simplify $\sqrt{25x^{10}}$?
4. How do fractional exponents relate to radicals?
5. What is the general formula for simplifying $\sqrt{a^m b^n}$?

Tip:

Always check if both numerical and variable terms under the radical can be simplified separately. This helps in applying radical properties more easily.