If \(A=-\sqrt{185}\), \(B=-13.6\), and \(C=-\frac{68}{5}\), which point lies farthest to the left on the number line?
Answer and explanation
Correct answer: Point A
Since \(C=-\frac{68}{5}=-13.6\), points \(B\) and \(C\) coincide. Also, \(13.6^2=184.96<185\), so \(\sqrt{185}>13.6\), which gives \(-\sqrt{185}<-13.6\). On a number line, the smaller number lies farther left; hence point \(A\) is farthest left. Exam tip: For negative numbers, the one with the greater absolute value is the smaller number.
Frequently asked questions
What is the correct answer to this question?
Point A
Why is this the correct answer?
Since \(C=-\frac{68}{5}=-13.6\), points \(B\) and \(C\) coincide. Also, \(13.6^2=184.96<185\), so \(\sqrt{185}>13.6\), which gives \(-\sqrt{185}<-13.6\). On a number line, the smaller number lies farther left; hence point \(A\) is farthest left. Exam tip: For negative numbers, the one with the greater absolute value is the smaller number.
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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