3√2- 2/(√2) =

Rationale

3√2 - 2/(√2) simplifies to 2√2.

To simplify the expression, we first rewrite the term 2/(√2) as √2, leading to the calculation 3√2 - √2, which results in 2√2.

A (2√2) CORRECT

This choice is the correct answer, as the simplification process yields 3√2 - √2 = 2√2. This shows that we have two times the square root of 2 after combining the like terms.

B (√2) YOUR ANSWER

This option is incorrect because it suggests that the result of simplifying 3√2 - 2/(√2) is simply √2. However, after simplification, we find that we actually have 2√2, which is larger than √2.

C (3) YOUR ANSWER

This choice is also incorrect as it implies that the expression simplifies to a whole number. The original expression contains square root terms, and after simplification, we arrive at a result involving √2, not a whole number.

D (4) YOUR ANSWER

This option is incorrect, as it indicates a value larger than what results from the simplification. The expression does not equate to a whole number like 4, but rather simplifies to 2√2, which is less than 4.

Conclusion

The simplification of the expression results in 2√2, confirming that this is the correct answer. Other choices fail to reflect the proper calculations involved in the expression, demonstrating that understanding the operations with roots is crucial for accurate simplification.

3√2- 2/(√2) =

3√2 - 2/(√2) simplifies to 2√2.

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