Which statement is correct when comparing \(3-\sqrt{2}\) and \(\frac{8}{5}\) on the number line?
Answer and explanation
Correct answer: \(3-\sqrt{2}<\frac{8}{5}\)
To compare the two numbers, rewrite \(3-\sqrt{2}<\frac{8}{5}\) as \(\sqrt{2}>\frac{7}{5}\). Both sides are positive, and \(2=\frac{50}{25}>\frac{49}{25}=\left(\frac{7}{5}\right)^2\), so \(\sqrt{2}>\frac{7}{5}\). Hence \(3-\sqrt{2}<\frac{8}{5}\). Their approximate values, \(1.586\) and \(1.6\), confirm this; therefore option B is incorrect. Exam tip: check that both sides are non-negative before squaring an inequality.
Frequently asked questions
What is the correct answer to this question?
\(3-\sqrt{2}<\frac{8}{5}\)
Why is this the correct answer?
To compare the two numbers, rewrite \(3-\sqrt{2}<\frac{8}{5}\) as \(\sqrt{2}>\frac{7}{5}\). Both sides are positive, and \(2=\frac{50}{25}>\frac{49}{25}=\left(\frac{7}{5}\right)^2\), so \(\sqrt{2}>\frac{7}{5}\). Hence \(3-\sqrt{2}<\frac{8}{5}\). Their approximate values, \(1.586\) and \(1.6\), confirm this; therefore option B is incorrect. Exam tip: check that both sides are non-negative before squaring an inequality.
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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