Which number is represented by \(\sqrt{\frac{196}{289}}\) on the number line?
Answer and explanation
Correct answer: \(\frac{14}{17}\)
Since \(196=14^2\) and \(289=17^2\), \(\sqrt{\frac{196}{289}}=\frac{\sqrt{196}}{\sqrt{289}}=\frac{14}{17}\). The square-root symbol denotes the principal, non-negative square root, so \(-\frac{14}{17}\) is not the value. Exam tip: when the numerator and denominator are perfect squares, take their positive square roots separately.
Frequently asked questions
What is the correct answer to this question?
\(\frac{14}{17}\)
Why is this the correct answer?
Since \(196=14^2\) and \(289=17^2\), \(\sqrt{\frac{196}{289}}=\frac{\sqrt{196}}{\sqrt{289}}=\frac{14}{17}\). The square-root symbol denotes the principal, non-negative square root, so \(-\frac{14}{17}\) is not the value. Exam tip: when the numerator and denominator are perfect squares, take their positive square roots separately.
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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