Question

The value of \[\left\{ \left( 23 + 2^2 \right)^{2/3} + (140 - 19 )^{1/2} \right\}^2 ,\] is 

Options

• 196

• 289

• 324

• 400

Answer 1

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`