If \(P=-\sqrt{80}\), between which two consecutive integers is \(P\) located?
Answer and explanation
Correct answer: Between \(-9\) and \(-8\)
The governing concept is locating a negative irrational number by bounding its positive square root. Since \(64<80<81\), taking square roots gives \(8<\sqrt{80}<9\). Negating reverses the order, so \(-9<-sqrt{80}<-8\). Thus \(P\) lies strictly between \(-9\) and \(-8\), making option A correct. Option C describes the corresponding positive root, not P. Option B places the value too close to zero, and option D places it below -9; neither agrees with the bounds obtained from 64 and 81.
Frequently asked questions
What is the correct answer to this question?
Between \(-9\) and \(-8\)
Why is this the correct answer?
The governing concept is locating a negative irrational number by bounding its positive square root. Since \(64<80<81\), taking square roots gives \(8<\sqrt{80}<9\). Negating reverses the order, so \(-9<-sqrt{80}<-8\). Thus \(P\) lies strictly between \(-9\) and \(-8\), making option A correct. Option C describes the corresponding positive root, not P. Option B places the value too close to zero, and option D places it below -9; neither agrees with the bounds obtained from 64 and 81.
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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