Question
The value of $\sqrt{5+2\sqrt6},$ is:
✓
Answer
- $\sqrt3+\sqrt2$
Solution:
$\sqrt{5+2\sqrt6}$
$=\sqrt{3+2+2\big(\sqrt3\big)\big(\sqrt2\big)}$
$=\sqrt{\big(\sqrt3\big)^2+\big(\sqrt2\big)^2-2\big(\sqrt3\big)\big(\sqrt2\big)}$
$=\sqrt{\big(\sqrt2+\sqrt2\big)^2}$
$=\sqrt3+\sqrt2$
Hence, correct option is (b).
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