Question

The value of `sqrt(248 + sqrt(52 + sqrt(144)` is ______.

विकल्प

• 14

• 12

• 16

• 13

Answer 1

The value of `sqrt(248 + sqrt(52 + sqrt(144)` is 16.

Explanation:

144 = 2 × 2 × 2 × 2 × 3 × 3

= (2 × 2 × 3)²

= 12²

∴ `sqrt(144) = 12`

∴ `sqrt(248 + sqrt(52 + sqrt(144))) = sqrt(248 + sqrt(52 + 12))`

= `sqrt(248 +sqrt( 64))`   ...(i)

Also, 64 = 2 × 2 × 2 × 2 × 2 × 2

=  (2 × 2 × 2)²

= 8²

`\implies sqrt(64) = 8`

∴ From (i), we get

`sqrt(248 + sqrt(52 + sqrt(144))) = sqrt(248 + 8`

= `sqrt(256)`  ...(ii)

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= (2 × 2 × 2 × 2)²

= (16)² 

`\implies sqrt(256) = 16`

∴ From (ii), we get

`sqrt(248 + sqrt(52 + sqrt(144))) = 16`