MCQ
The value of $\sqrt{5-2 \sqrt{6}}$ is
- ✓$\sqrt{3}-\sqrt{2}$
- B$\sqrt{2}-\sqrt{3}$
- C$\sqrt{5}-\sqrt{6}$
- D$\sqrt{5}+\sqrt{6}$
✓
Answer
Correct option: A.
$\sqrt{3}-\sqrt{2}$
(a)
$\sqrt{5-2 \sqrt{6}}=\sqrt{3+2-2 \sqrt{3 \times 2}}=\sqrt{(\sqrt{3})^2+(\sqrt{2})^2-2 \sqrt{3} \sqrt{2}}=\sqrt{(\sqrt{3}-\sqrt{2})^2}=\sqrt{3}-\sqrt{2}$
$\sqrt{5-2 \sqrt{6}}=\sqrt{3+2-2 \sqrt{3 \times 2}}=\sqrt{(\sqrt{3})^2+(\sqrt{2})^2-2 \sqrt{3} \sqrt{2}}=\sqrt{(\sqrt{3}-\sqrt{2})^2}=\sqrt{3}-\sqrt{2}$
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