Question 19

√(1/11^2 + 1/14^2)

The expression simplifies to √(1/11^2 + 1/14^2), which is the correct option E. This result arises from manipulating the square roots and applying algebraic identities.

A) 1/(11)(14)

Option A is incorrect because it does not correctly represent the simplification of the original expression. The expression involves square roots and squares, which cannot be reduced to a simple multiplication of the denominators without considering the square roots.

B) 11/11 + 14/14

Option B is also incorrect. While it simplifies to 1 + 1, it fails to relate to the original expression, which involves square roots and is not reducible to a simple addition of fractions.

C) 1/11^2 + 1/14^2

Option C is incorrect as it does not take the square root of the sum of the squares. The correct answer is the square root of the sum, not the sum of the reciprocals of the squares themselves.

D) √(1/11 + 1/14)

Option D is incorrect because it incorrectly simplifies the expression. The proper operation involves squaring 11 and 14, and then summing those squared terms under a single square root.

E) √(1/11^2 + 1/14^2)

Option E is correct as it accurately represents the final form of the expression after simplification. It captures the necessary combination of the components of the original expression.

Conclusion

Option E is the definitive correct answer as it properly reflects the operations required to simplify the original expression. All other options fail to demonstrate the correct application of square roots and algebraic manipulation, confirming that they do not meet the criteria established by the problem.