Question 20

3√2 - 2/(√2) = 2√2

To simplify the expression 3√2 - 2/(√2), we first rewrite 2/(√2) as √2. This leads to the equation 3√2 - √2, which simplifies to 2√2.

A) 2√2

This option is correct as the expression simplifies directly to 3√2 - √2, resulting in 2√2. The arithmetic operation is valid, confirming that this is indeed the right answer.

B) √2

This option is incorrect. While it resembles part of the simplification, it does not represent the final result of the expression. The subtraction of √2 from 3√2 does not yield √2.

C) 3

This option is incorrect. The expression involves square roots and cannot be simplified to a whole number like 3. The calculations show that the result is a multiple of √2.

D) 4

This option is incorrect. The expression involves roots and subtraction, leading to a value much less than 4. The calculation shows that the final result aligns with the square root values rather than a whole number.

Conclusion

The correct answer, 2√2, is derived from the proper simplification of the expression. All other options fail to represent the outcome of the calculation, demonstrating a fundamental understanding of arithmetic operations involving square roots.