MCQ
The value of $\sqrt{248+\sqrt{52+\sqrt{144}}}$ is:
- A$14$
- B$12$
- ✓$16$
- D$13$
✓
Answer
Correct option: C.
$16$
We have, $\sqrt{248+\sqrt{52+\sqrt{144}}}$
$=\sqrt{248+\sqrt{52+12}}$ $[\because$ square root of $144 = 12$$]$
$=\sqrt{248+\sqrt{64}}$
$=\sqrt{248+8}$ $[\because$ square root of $64 = 8$$]$
$=\sqrt{256}=16$ $[\because$ square root of $256 = 16$$]$
$=\sqrt{248+\sqrt{52+12}}$ $[\because$ square root of $144 = 12$$]$
$=\sqrt{248+\sqrt{64}}$
$=\sqrt{248+8}$ $[\because$ square root of $64 = 8$$]$
$=\sqrt{256}=16$ $[\because$ square root of $256 = 16$$]$
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