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Question
The value of \[\left\{ \left( 23 + 2^2 \right)^{2/3} + (140 - 19 )^{1/2} \right\}^2 ,\] is
Options
196
289
324
400
Solution
We have to find the value of `{(23+2^2)^(2/3)+ (140- 19 )^(1/2) }^2`
`{(23+2^2)^(2/3)+ (140- 19 )^(1/2) }^2 = {(23+4)^(2/3)+ (121)^(1/2) }^2`
= `{(27)^(2/3)+ (121)^(1/2) }^2`
`={(3^3)^(2/3)+ (11^2)^(1/2) }^2`
`{(23+2^2)^(2/3)+ (140- 19 )^(1/2) }^2`= ` {3^(3 xx2/3) +11
^( 2xx 1/2)}^2`
` = {3^(3 xx2/3) +11^( 2xx 1/2)}^2`
= `{3^2 + 11}^2`
`⇒ {(23+2^2)^(2/3)+ (140- 19 )^(1/2) }^2 = {9+11}^2`
By using the identity `(a+b)^2 = a^2 +2ab +b^2` we get,
`= 9 xx 9 +2 xx 9 xx 11 + 11 xx 11`
`= 81 +198 +121`
`= 400`
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