Select **ALL** the expressions that are true.

Answer choices:

√(n2) = n

-n + n = 0

**-n**/**-n** = 1

5n = **n**/**5**

n cubed = n2

(-n)2 = n2

-n3 = n3

√(n)(0) = 0

Let's analyze each expression one by one:

1. **√(n²) = n**  
   This expression is **false**.  
   The square root of \( n^2 \) is \( |n| \), the absolute value of \( n \). So, \( \sqrt{n^2} = |n| \), not \( n \), because \( n \) could be negative, but \( |n| \) is always positive.

2. **-n + n = 0**  
   This expression is **true**.  
   For any number \( n \), adding its opposite results in 0. \( -n + n = 0 \).

3. **-n / -n = 1**  
   This expression is **true**.  
   Dividing a number by itself (provided \( n \neq 0 \)) gives 1, and the negatives cancel out.

4. **5n = n / 5**  
   This expression is **false**.  
   \( 5n \) is 5 times \( n \), while \( n / 5 \) is \( n \) divided by 5. They are not equal.

5. **n cubed = n²**  
   This expression is **false**.  
   \( n^3 \) and \( n^2 \) are not equal. \( n^3 \) is \( n \times n \times n \), while \( n^2 \) is \( n \times n \).

6. **(-n)² = n²**  
   This expression is **true**.  
   Squaring \( -n \) results in \( n^2 \), since \( (-n) \times (-n) = n^2 \).

7. **-n³ = n³**  
   This expression is **false**.  
   The cube of a negative number is negative, so \( -n^3 \neq n^3 \).

8. **√(n)(0) = 0**  
   This expression is **true**.  
   Any number multiplied by 0 is 0, so \( \sqrt{n} \times 0 = 0 \).

### Summary of True Expressions:
- **-n + n = 0**
- **-n / -n = 1**
- **(-n)² = n²**
- **√(n)(0) = 0**

Would you like more details or have any questions?

Here are five related questions to explore further:
1. What happens if you take the square root of a negative number?
2. How does squaring a negative number differ from cubing it?
3. What is the difference between multiplying and dividing variables?
4. Can you simplify expressions involving absolute values?
5. What properties do even and odd exponents have?

**Tip:** When working with square roots, always consider the absolute value for non-negative results.

Select ALL the expressions that are true.

√(n²) = n

-n + n = 0

-n / -n = 1

5n = n / 5

n cubed = n²

(-n)² = n²

-n³ = n³

√(n)(0) = 0

Analyze which mathematical expressions involving square roots, exponents, and basic arithmetic are true. This problem covers important algebraic concepts such as √(n²) = |n|, properties of exponents, and arithmetic operations. Suitable for Grades 9-11.

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