https://r2.erweima.ai/mathbot/image/1726702935364983isqcg.jpg

The image shows a mathematical expression under a nested square root. The expression is:

\[
\sqrt{\frac{\sqrt{8}}{2}}
\]

Now let's simplify this step by step:

1. Simplify \(\sqrt{8}\):
   \[
   \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
   \]

2. Now substitute this into the expression:
   \[
   \sqrt{\frac{2\sqrt{2}}{2}}
   \]

3. Simplify the fraction:
   \[
   \frac{2\sqrt{2}}{2} = \sqrt{2}
   \]

4. Finally, the square root of \(\sqrt{2}\):
   \[
   \sqrt{\sqrt{2}} = 2^{1/4}
   \]

Therefore, the simplified result is:

\[
2^{1/4} \approx 1.189
\]

Let me know if you'd like more details or have any questions!

### Related Questions:
1. What is the value of \(\sqrt{8}\) in decimal form?
2. How does the property of radicals help in simplifying nested square roots?
3. What are some common properties of square roots used in simplifications?
4. How does \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\) apply in this context?
5. Can fractional exponents be used to express roots more efficiently?

**Tip:** Simplifying inside a radical before taking further roots is a key strategy in radical expressions.

The query submitted by the user: What is the expression shown in the image and how can it be simplified?

Explore how to simplify the expression sqrt(sqrt(8)/2) step by step, using basic properties of radicals and exponents. This page offers a detailed guide suitable for high school students learning about radicals and exponents.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation