Which value lies between −√3 and −5/3 on the number line?
Answer and explanation
Correct answer: −1.70
The key concept is comparing negative real numbers in their actual number-line order. Since √3≈1.732, we have -√3≈-1.732. Also, -5/3=-1.6666... . A number between these endpoints must be greater than -1.732 and less than -1.6666..., because the more negative number is farther to the left. Among the choices, -1.70 satisfies -1.732<-1.70<-1.6666..., so it lies between the two given values. Therefore option A is correct. The value -1.60 is to the right of the interval, while -1.80 and -2.00 are more negative and lie to its left. Treating the negative values as positive magnitudes would reverse the comparison incorrectly.
Frequently asked questions
What is the correct answer to this question?
−1.70
Why is this the correct answer?
The key concept is comparing negative real numbers in their actual number-line order. Since √3≈1.732, we have -√3≈-1.732. Also, -5/3=-1.6666... . A number between these endpoints must be greater than -1.732 and less than -1.6666..., because the more negative number is farther to the left. Among the choices, -1.70 satisfies -1.732<-1.70<-1.6666..., so it lies between the two given values. Therefore option A is correct. The value -1.60 is to the right of the interval, while -1.80 and -2.00 are more negative and lie to its left. Treating the negative values as positive magnitudes would reverse the comparison incorrectly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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