Question

$\sqrt{24 + 2\sqrt{143} }= ?$

• A. $\sqrt{2} + \sqrt{13}$
• B. $\sqrt{3} + \sqrt{13}$
• C. $\sqrt{7} + \sqrt{13}$
• D. $\sqrt{11} + \sqrt{13}$

Hint:

$\sqrt{(x+y) + 2\sqrt{xy}} = \sqrt{x} + \sqrt{y}$.

Answer 1

The Correct Option is D

Step 1: Concept
Square root of a surd in the form $\sqrt{a + 2\sqrt{b}}$.

Step 2: Analysis
We need two numbers whose sum is 24 and product is 143.

Step 3: Calculation
$11 + 13 = 24$ and $11 \times 13 = 143$.
$\sqrt{(\sqrt{11})^2 + (\sqrt{13})^2 + 2\sqrt{11}\sqrt{13}} = \sqrt{(\sqrt{11} + \sqrt{13})^2}$.

Step 4: Conclusion
The value is $\sqrt{11} + \sqrt{13}$. Final Answer: (D)