Question

the simplified value of (root 12-root 8) (root 3+root 2)/5+ root 24 the whole root

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ \sqrt{ \frac{( \sqrt{12} - \sqrt{8})( \sqrt{3} + \sqrt{2} ) }{5 + \sqrt{24} } } }$

EVALUATION

$\displaystyle \sf{ \sqrt{ \frac{( \sqrt{12} - \sqrt{8})( \sqrt{3} + \sqrt{2} ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{( \sqrt{2 \times 2 \times 3} - \sqrt{2 \times 2 \times 2})( \sqrt{3} + \sqrt{2} ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{(2 \sqrt{ 3} - 2 \sqrt{2 })( \sqrt{3} + \sqrt{2} ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2( \sqrt{ 3} - \sqrt{2 })( \sqrt{3} + \sqrt{2} ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2( {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2( 3 - 2 ) }{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2}{5 + \sqrt{24} } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2(5 - \sqrt{24} )}{(5 + \sqrt{24})(5 - \sqrt{24} ) } } }$

$= \displaystyle \sf{ \sqrt{ \frac{2(5 - \sqrt{24} )}{(25 - 24) } } }$

$= \displaystyle \sf{ \sqrt{2(5 - \sqrt{24} )} }$

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Answer 2

$\huge{\boxed{\bold{Question}}}$

the simplified value of (root 12-root 8) (root 3+root 2)/5+ root 24 the whole root

$\huge{\boxed{\bold{Åñswér}}}$

Solution,

The value of

$\longmapsto \sqrt{ \frac{(12 - \sqrt{8} )( \sqrt{3} + \sqrt{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{( \sqrt{12} - \sqrt{8})( \sqrt{3} + \sqrt{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{(2 \times 2 \times 3 - \sqrt{2 \times 2 \times 2} )( \sqrt{3 } + \sqrt{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{(2 \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{2( \sqrt{3 } - \sqrt{2} )( \sqrt{3} + \sqrt{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{2(( \sqrt{3}^{2} - ( \sqrt{2} ^{2} }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{ \sqrt{2} (3 - 2)}{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{ 2 }{5 + \sqrt{24} } } \\ \\ \\ \longmapsto \sqrt{ \frac{2(5 - \sqrt{24} }{5 + \sqrt{24} )(5 - \sqrt{24}) } } \\ \\ \\ \longmapsto\frac{2(5 - \sqrt{24} )}{(25 - 24)} \\ \\ \\ \longmapsto\sqrt{ 2(5 - \sqrt{24} }$

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