సరళీకరించండి:$$\sqrt {11 - 2\sqrt {30} }$$

1. $$\sqrt 6 + \sqrt 5$$
2. 6
3. $$\sqrt 6 - \sqrt 5$$
4. $$6 - \sqrt 5$$

Option 3 : $$\sqrt 6 - \sqrt 5$$
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Detailed Solution

$$\begin{array}{l} \sqrt {11 - 2\sqrt {30} } \\ = \sqrt {\left( {11} \right) - 2\sqrt 6 \times \sqrt 5 } \\ = \sqrt {\left( {6 + 5} \right) - 2\sqrt 6 \times \sqrt 5 } \\ = \sqrt {{{\left( {\sqrt 6 } \right)}^2} + {{\left( {\sqrt 5 } \right)}^2} - 2\sqrt 6 \times \sqrt 5 } \\ = \sqrt {{{\left( {\sqrt 6 - \sqrt 5 } \right)}^2}} \\ = \sqrt 6 - \sqrt 5 \end{array}$$

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