Question

Consider the following equations I and II. \[ \text{I} : \sqrt{1\frac{9}{16}} = 1\frac{1}{4} \] \[ \text{II} : \sqrt[3]{2744} = 2 \times 7\sqrt{7} \]

• A. I and II are correct
• B. I is incorrect, II is correct
• C. I is correct, II is incorrect
• D. I and II are incorrect

Hint:

Remember the perfect cube: \[ 14^3=2744 \] This allows you to evaluate $\sqrt[3]{2744}$ instantly.

Answer 1

The Correct Option is C

Concept: To verify the correctness of the given equations, evaluate both sides independently.

Step 1: Check Equation I. Convert the mixed fraction into an improper fraction: \[ 1\frac{9}{16}=\frac{16+9}{16}=\frac{25}{16} \] Taking square root: \[ \sqrt{\frac{25}{16}}=\frac{5}{4} \] Now, \[ 1\frac{1}{4}=\frac{5}{4} \] Hence, \[ \sqrt{1\frac{9}{16}}=1\frac{1}{4} \] Therefore, Equation I is correct.

Step 2: Check Equation II. \[ 2744=14^3 \] Therefore, \[ \sqrt[3]{2744}=14 \] But, \[ 2\times 7\sqrt7 = 14\sqrt7 \] Since \[ 14 \ne 14\sqrt7, \] Equation II is incorrect.

Step 3: Conclusion. Equation I is correct and Equation II is incorrect. \[ \boxed{\text{Option (C)}} \]