√171 - √19 =

Rationale

√171 - √19 = √76.

To solve the expression, we first simplify √171 and √19. The difference between these two square roots can be represented as √(171 - 19), which simplifies to √152. However, when calculating the numerical value, it is evident that √76 is the correct answer that accurately represents the result of the subtraction.

A (√152) YOUR ANSWER

This choice represents the square root of the difference calculated incorrectly as √(171 - 19). Although √152 is a resultant expression from the subtraction, it is not the simplified form that accurately represents the outcome of the operation, which leads to √76 instead.

B (√133) YOUR ANSWER

This option is incorrect as it does not correspond to any calculation derived from √171 - √19. The square root of 133 does not relate to either of the original square roots and does not result from any valid arithmetic operation involving them.

C (√95) YOUR ANSWER

This choice is also incorrect because √95 does not arise from the operation √171 - √19. The value 95 does not represent the difference between the two square roots, nor does it relate to the problem in any meaningful mathematical way.

D (√76) CORRECT

This is the correct choice, as √76 is the simplified form of the difference √171 - √19. It accurately reflects the result of the calculation, confirming that the operation leads to a valid square root.

Conclusion

The expression √171 - √19 simplifies down to √76, making it the correct answer. The other options, while related to square roots, do not accurately represent the result of the given operation. Understanding how to manipulate square roots and perform basic arithmetic operations is crucial for solving similar problems effectively.

√171 - √19 =

√171 - √19 = √76.

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