Which number has distance \(\sqrt{41}\) from 0 and lies to the left of 0 on the number line?
Answer and explanation
Correct answer: \(-\sqrt{41}\)
The governing concept is directed distance on a number line. A point at distance d from zero can have coordinate d or -d, because the two sides of zero are opposite directions. The phrase “to the left of 0” selects the negative coordinate. Here d = √41, so the required coordinate is -√41. Option B is therefore correct. Option A has the same distance from zero but lies to the right. Options C and D are not correct because their distances from zero are 41, not √41. Thus both the magnitude and the direction must be considered.
Frequently asked questions
What is the correct answer to this question?
\(-\sqrt{41}\)
Why is this the correct answer?
The governing concept is directed distance on a number line. A point at distance d from zero can have coordinate d or -d, because the two sides of zero are opposite directions. The phrase “to the left of 0” selects the negative coordinate. Here d = √41, so the required coordinate is -√41. Option B is therefore correct. Option A has the same distance from zero but lies to the right. Options C and D are not correct because their distances from zero are 41, not √41. Thus both the magnitude and the direction must be considered.
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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