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Question
The value of `sqrt(248 + sqrt(52 + sqrt(144)` is ______.
Options
14
12
16
13
Solution
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`
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