https://file.aiquickdraw.com/mathbot/file/17256917963924u5f8gao.jpg

Let's simplify the given expression step by step. The expression is:

\[
\left( 21 - \sqrt{100} \right) \div 11 + | -6 | \div \frac{1}{6} - 3^2
\]

### Step 1: Simplify \(\sqrt{100}\)
\[
\sqrt{100} = 10
\]

Now the expression becomes:
\[
(21 - 10) \div 11 + | -6 | \div \frac{1}{6} - 3^2
\]

### Step 2: Simplify inside parentheses
\[
21 - 10 = 11
\]

Now the expression is:
\[
11 \div 11 + | -6 | \div \frac{1}{6} - 3^2
\]

### Step 3: Simplify absolute value
\[
| -6 | = 6
\]

The expression now becomes:
\[
11 \div 11 + 6 \div \frac{1}{6} - 3^2
\]

### Step 4: Simplify the first division
\[
11 \div 11 = 1
\]

Now the expression is:
\[
1 + 6 \div \frac{1}{6} - 3^2
\]

### Step 5: Simplify the second division
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
6 \div \frac{1}{6} = 6 \times 6 = 36
\]

Now the expression becomes:
\[
1 + 36 - 3^2
\]

### Step 6: Simplify the exponent
\[
3^2 = 9
\]

Now the expression is:
\[
1 + 36 - 9
\]

### Step 7: Perform the final operations
\[
1 + 36 = 37
\]
\[
37 - 9 = 28
\]

### Final Answer:
The simplified expression is:
\[
\boxed{28}
\]

Would you like more details or explanations on any step? Here are 5 related questions for practice:

1. Simplify \(\sqrt{49} + | -7 | - 2^3\).
2. What is the value of \((25 - \sqrt{81}) \div 11 + | -9 |\)?
3. Simplify \(15 \div 5 + 2^3 - | -8 |\).
4. Solve \(\frac{36}{\sqrt{36}} + 3^2 - | -3 |\).
5. Simplify \((18 - \sqrt{144}) \div 6 + | -5 |^2\).

**Tip:** When simplifying expressions, always perform operations inside parentheses and exponents before handling addition, subtraction, or division!

Simplify the expression: (21 - √100) ÷ 11 + | -6 | ÷ (1/6) - 3^2

Simplify the mathematical expression (21 - √100) ÷ 11 + | -6 | ÷ (1/6) - 3^2 with step-by-step instructions. This problem involves square roots, absolute values, division of fractions, exponents, and follows the order of operations (PEMDAS). Suitable for middle school students (Grades 6-8).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation