To solve the expression [tex]\( \sqrt{18} + \sqrt{2} \)[/tex] and determine which statement is true, let's break down the solution step by step.
1. Simplify [tex]\( \sqrt{18} \)[/tex]:
- We can rewrite [tex]\( \sqrt{18} \)[/tex] as [tex]\( \sqrt{9 \cdot 2} \)[/tex].
- Since [tex]\( 9 \)[/tex] is a perfect square, [tex]\( \sqrt{9} = 3 \)[/tex].
- Therefore, [tex]\( \sqrt{18} = \sqrt{9 \cdot 2} = 3 \sqrt{2} \)[/tex].
2. Combine the terms:
- The expression becomes [tex]\( 3 \sqrt{2} + \sqrt{2} \)[/tex].
- Both terms have the common factor [tex]\( \sqrt{2} \)[/tex].
3. Add like terms:
- [tex]\( 3 \sqrt{2} + \sqrt{2} \)[/tex] can be simplified by combining the coefficients.
- This gives us [tex]\( (3 + 1) \sqrt{2} = 4 \sqrt{2} \)[/tex].
So, the original expression [tex]\( \sqrt{18} + \sqrt{2} \)[/tex] simplifies to [tex]\( 4 \sqrt{2} \)[/tex].
### Conclusion:
The expression [tex]\( \sqrt{18} + \sqrt{2} \)[/tex] is irrational and equal to [tex]\( 4 \sqrt{2} \)[/tex].
Therefore, the correct statement is:
- It is irrational and equal to [tex]\( 4 \sqrt{2} \)[/tex].
