If \(\sqrt{a}\) lies between 5 and 6 on the number line, what is the range of \(a\)?
Answer and explanation
Correct answer: \(25<a<36\)
We are given \(5<\sqrt{a}<6\). Since all quantities are positive, squaring all three parts preserves the inequality and gives \(25<a<36\). Option A incorrectly treats the range of \(\sqrt{a}\) as the range of \(a\). Exam tip: for positive bounds involving a square root, square both boundary values.
Frequently asked questions
What is the correct answer to this question?
\(25<a<36\)
Why is this the correct answer?
We are given \(5<\sqrt{a}<6\). Since all quantities are positive, squaring all three parts preserves the inequality and gives \(25<a<36\). Option A incorrectly treats the range of \(\sqrt{a}\) as the range of \(a\). Exam tip: for positive bounds involving a square root, square both boundary values.
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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