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The value of \(\frac{{\sqrt {\sqrt {21 - 9\sqrt 5 } \times \sqrt {21 + 9\sqrt 5 } } }}{{\sqrt {12} \times \sqrt {\left( {18 - 8\sqrt 5 } \right) \times \left( {18 + 8\sqrt 5 } \right)} }}\)1). \(\frac{1}{2}\)2). 23). \(\frac{1}{{2\sqrt 2 }}\)4). \(\frac{1}{{\sqrt 2 }}\) |
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Answer» Numerator of expression = √ (√ (21 - 9√5) × √ (21 + 9√5)) ⇒ √ (√ (212 – (9√5)2)) = √ (√ (441 – 405)) = √ (√ 36) = √6 Denominator of equation = √ (12 × √ (18 - 8√5) × √ (18 + 8√5)) ⇒ √ 12 × √ (182 - (8√5)2) = √12 × √ (324 - 320) = √12 × √4 = 2√12 So, $(\frac{{\sqrt {\sqrt {21 - 9\sqrt 5 } \times \sqrt {21 + 9\sqrt 5 } } }}{{\sqrt {12} \times \sqrt {\LEFT( {18 - 8\sqrt 5 } \RIGHT) \times \left( {18 + 8\sqrt 5 } \right)} }} = \frac{{\sqrt 6 }}{{2\sqrt {12} }} = \frac{1}{{2\sqrt 2 }})$ |
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