Which of the following is the value of \(\sqrt{\frac{49}{64}}\)?
Answer and explanation
Correct answer: \(\frac{7}{8}\)
Use the rule \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) for nonnegative \(a,b\). So \(\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}\). The principal square root is nonnegative, so \(-\frac{7}{8}\) is not valid. The other distractors come from incorrect manipulation (for example taking root only of numerator or misplaced division). Exam tip: simplify perfect squares in numerator and denominator before taking the square root, and remember the principal root is positive.
Frequently asked questions
What is the correct answer to this question?
\(\frac{7}{8}\)
Why is this the correct answer?
Use the rule \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) for nonnegative \(a,b\). So \(\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}\). The principal square root is nonnegative, so \(-\frac{7}{8}\) is not valid. The other distractors come from incorrect manipulation (for example taking root only of numerator or misplaced division). Exam tip: simplify perfect squares in numerator and denominator before taking the square root, and remember the principal root is positive.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
