Question 12

√171 - √19 = √76

The expression √171 - √19 simplifies to √76, indicating that the difference between these two square roots results in this specific square root value.

A) √152

Option A is incorrect because √152 does not equal the result of √171 - √19. In fact, √152 is greater than √171 - √19, indicating that it is not the correct simplification of the expression.

B) √133

Option B is also incorrect. The value of √133 is not equivalent to the difference between √171 and √19. This option represents a value that does not align with the calculated result of the expression.

C) √95

Option C is incorrect since √95 does not represent the difference between √171 and √19. This option yields a value that is less than the actual result of the expression, making it an unsuitable choice.

D) √76

Option D is correct because it accurately represents the result of the expression √171 - √19. This option is the only one that correctly simplifies the given square root difference.

Conclusion

The correct answer, √76, is the valid simplification of the expression √171 - √19. All other options fail to represent the correct value, either being larger or smaller than the actual result. Thus, D is definitively the right choice based on the mathematical operations involved.