Let's simplify the expression step by step:

Given expression:  
\[
\sqrt{\sqrt{3^6}}
\]

### Step 1: Simplify \( 3^6 \)
\[
3^6 = 729
\]

Now, the expression becomes:
\[
\sqrt{\sqrt{729}}
\]

### Step 2: Simplify the inner square root
\[
\sqrt{729} = 27
\]

So, now the expression is:
\[
\sqrt{27}
\]

### Step 3: Simplify \( \sqrt{27} \)
\[
\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}
\]

Thus, the final simplified form of the expression is:
\[
3\sqrt{3}
\]

Would you like more details on any of the steps or have any questions?

Here are five related questions:
1. How do you simplify nested square roots in general?
2. Can you solve \( \sqrt{81} \) using the same process?
3. What is the result of \( \sqrt{\sqrt{2^8}} \)?
4. How do you simplify \( \sqrt{a^2} \) for any value of \( a \)?
5. Can you explain how to handle cube roots in a similar way?

**Tip:** Always simplify powers inside a root before taking the square root itself!

Discover how to simplify nested square roots in the expression √(√(3^6)) with step-by-step instructions. This example involves exponentiation and radical properties, making it suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation