Discussion
Find the square root of \(1\frac{56}{169}\).
Answer: C
The square root is \(1\frac{2}{13}\).
Convert the mixed number to an improper fraction, then take the square roots of numerator and denominator separately.
\[ \begin{aligned} 1\tfrac{56}{169} &= \tfrac{169 + 56}{169} = \tfrac{225}{169} \\ \sqrt{\tfrac{225}{169}} &= \tfrac{15}{13} = 1\tfrac{2}{13} \end{aligned} \]
Check: \(\left(\frac{15}{13}\right)^{2} = \frac{225}{169}\). \(1\frac{1}{13} = \frac{14}{13}\) squares to \(\frac{196}{169}\), too small, and the options beginning with 2 square to more than 4, far too large.
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