\(\sqrt{3 + 2 \sqrt{2}}\) - \(\sqrt{3 - 2 \sqrt{2}}\)  সমান:

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UP TGT Mathematics 2019 Official Paper
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  1. 1
  2. \(\sqrt{3} + 1\)
  3. \(\sqrt{3} - 1\)
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2
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Detailed Solution

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প্রদত্ত:

\(X=\sqrt{3 + 2 \sqrt{2}}-\sqrt{3 - 2 \sqrt{2}}\)

\(=\sqrt {{(2 + 1) + 2} \sqrt 2}-\sqrt {{(2 + 1) - 2} \sqrt 2}\)

\(=\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} + 2\sqrt 2}-\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} - 2\sqrt 2}\)

\(=\sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}}-\sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}}\)

= √2 + 1 – (√2 – 1)

= 2

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