Which number has distance \(\sqrt{26}\) from 0 and lies to the right of 0 on the number line?
Answer and explanation
Correct answer: \(\sqrt{26}\)
The governing concept is absolute distance on a number line. A point at distance \(d\) from zero can be either \(d\) or \(-d\), because both have absolute value \(d\). Here the distance is \(\sqrt{26}\), so the two possible points are \(\sqrt{26}\) and \(-\sqrt{26}\). The condition that the point lies to the right of zero selects the positive value, \(\sqrt{26}\). Therefore option B is correct. Option A has the required distance but lies left of zero; options C and D have distance 26, not \(\sqrt{26}\).
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{26}\)
Why is this the correct answer?
The governing concept is absolute distance on a number line. A point at distance \(d\) from zero can be either \(d\) or \(-d\), because both have absolute value \(d\). Here the distance is \(\sqrt{26}\), so the two possible points are \(\sqrt{26}\) and \(-\sqrt{26}\). The condition that the point lies to the right of zero selects the positive value, \(\sqrt{26}\). Therefore option B is correct. Option A has the required distance but lies left of zero; options C and D have distance 26, not \(\sqrt{26}\).
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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