Answered

An expression is shown below:
[tex]\[ \sqrt{18} + \sqrt{2} \][/tex]

Which statement is true about the expression?

A. It is rational and equal to 3.
B. It is rational and equal to 4.
C. It is irrational and equal to [tex]\( 3 \sqrt{2} \)[/tex].
D. It is irrational and equal to [tex]\( 4 \sqrt{2} \)[/tex].



Answer :

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].