0 vote
Find the value of \(\sqrt { - \sqrt 6 + \sqrt {15 + 18\sqrt {22 + 8\sqrt 6 } } } \)
Find the value of \(\sqrt { - \sqrt 6 + \sqrt {15 + 18\sqrt {22 + 8\sqrt 6 } } } \)
1). 9
2). 6
3). 5
4). 3
1 answers
1 vote
We know that,
$(\begin{array}{l} = \;\sqrt { - \sqrt 6 \; + \;\sqrt {15\; + \;18\sqrt {22\; + \;8\sqrt 6 } } } \;\\ = \;\sqrt { - \sqrt 6 \; + \;\sqrt {15\; + \;18\sqrt {16\; + \;6\; + \;2\left( 4 \right)(\sqrt 6 } } )\;} \;\\ = \;\sqrt { - \sqrt 6 \; + \;\sqrt {15\; + \;18\left( {4\; + \;\sqrt 6 } \right)} } \\ = \;\sqrt { - \sqrt 6 \; + \;\sqrt {15\; + \;72\; + \;18\sqrt 6 } } \;\\ = \;\sqrt { - \sqrt 6 \; + \;\sqrt {87\; + \;18\sqrt 6 } } \;\\ = \;\sqrt { - \sqrt 6 \; + \;\sqrt {81\; + \;6\; + \;2\left( 9 \right)\left( {\sqrt 6 } \right)} } \;\\ = \;\sqrt { - \sqrt 6 \; + \;9\; + \;\sqrt 6 } \; = \;\sqrt 9 \; = \;3 \end{array})$