Certainly! Let's solve this step-by-step:
1. Understand and Simplify the Expression:
The given expression is [tex]\( 0 \cdot \sqrt{5} \)[/tex].
- Multiplication by Zero: Any number multiplied by zero is always zero. So, the expression [tex]\( 0 \cdot \sqrt{5} \)[/tex] simplifies to [tex]\( 0 \)[/tex].
2. Simplified Expression:
After simplification, the expression becomes [tex]\( 0 \)[/tex].
3. Determine if the Result is Rational or Irrational:
- Rational Numbers: A rational number is any number that can be expressed as the fraction [tex]\( \frac{a}{b} \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are integers, and [tex]\( b \neq 0 \)[/tex]. Examples of rational numbers include [tex]\( \frac{1}{2} \)[/tex], [tex]\( -3 \)[/tex], [tex]\( \frac{7}{1} \)[/tex], and [tex]\( 0 \)[/tex] (since [tex]\( 0 \)[/tex] can be written as [tex]\( \frac{0}{1} \)[/tex]).
- Irrational Numbers: An irrational number cannot be expressed as a simple fraction. Examples include [tex]\( \sqrt{2} \)[/tex], [tex]\( \pi \)[/tex], and [tex]\( e \)[/tex].
Since [tex]\( 0 \)[/tex] can be written as [tex]\( \frac{0}{1} \)[/tex], it is a rational number.
4. Conclusion:
The simplified expression is [tex]\( 0 \)[/tex], and [tex]\( 0 \)[/tex] is a rational number.
Therefore, the result of the expression [tex]\( 0 \cdot \sqrt{5} \)[/tex] is [tex]\( 0 \)[/tex], and it is a rational number.
