Amanita, let's solve each problem inside the green rectangle step by step. Here’s my plan:

Step-by-step Plan:

1. For each expression, I will first rewrite it in mathematical notation.
2. I will then simplify or calculate the value using the properties of exponents and square roots.
3. I will explain each step in detail, using the correct formulas and math expressions.

Let's begin:

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(1) $(\sqrt{5})^2$

• The square of a square root cancels out the root: $(\sqrt{a})^2 = a$.
• So, $(\sqrt{5})^2 = 5$.

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(2) $(- \sqrt{11})^2$

• The square of a negative number is positive: $( -a )^2 = a^2$.
• The square of a square root: $(\sqrt{a})^2 = a$.
• So, $(- \sqrt{11})^2 = ( -1 \times \sqrt{11} )^2 = ( -1 )^2 \times (\sqrt{11})^2 = 1 \times 11 = 11$.

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(3) $\sqrt{ \left( \frac{3}{4} \right)^2 }$

• The square root of a square: $\sqrt{a^2} = |a|$ (the absolute value of $a$).
• So, $\sqrt{ \left( \frac{3}{4} \right)^2 } = \left| \frac{3}{4} \right| = \frac{3}{4}$.

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(4) $\sqrt{2.6}$

• This is simply the square root of 2.6. I will calculate its value.

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Now, I will calculate and confirm each answer. Amanita, here are the detailed solutions for each problem:

1. $(\sqrt{5})^2 = 5$

   • When you square a square root, you get the number inside the root.

2. $(- \sqrt{11})^2 = 11$

   • Squaring a negative number makes it positive, and squaring the square root gives the number inside.

3. $\sqrt{ \left( \frac{3}{4} \right)^2 } = \frac{3}{4}$

   • The square root of a square gives the absolute value, and since $\frac{3}{4}$ is positive, the answer is $\frac{3}{4}$.

4. $\sqrt{2.6} \approx 1.61$

   • The square root of 2.6 is about 1.61 (rounded to two decimal places).

If you have any more questions or need further explanations, let me know!