After squaring \(\sqrt{3}=\frac{r}{s}\), which equation is correct?
Answer and explanation
Correct answer: \(r^2=3s^2\)
Squaring both sides of \(\sqrt{3}=\frac{r}{s}\) gives \(3=\frac{r^2}{s^2}\). Multiplying both sides by \(s^2\) gives \(r^2=3s^2\), so option C is correct. In option B, the relationship is reversed. Exam tip: after squaring an equation involving a fraction, multiply by the square of the denominator to remove the fraction.
Frequently asked questions
What is the correct answer to this question?
\(r^2=3s^2\)
Why is this the correct answer?
Squaring both sides of \(\sqrt{3}=\frac{r}{s}\) gives \(3=\frac{r^2}{s^2}\). Multiplying both sides by \(s^2\) gives \(r^2=3s^2\), so option C is correct. In option B, the relationship is reversed. Exam tip: after squaring an equation involving a fraction, multiply by the square of the denominator to remove the fraction.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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