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The smallest integer larger than (sqrt(3...

The smallest integer larger than `(sqrt(3) + sqrt(2))^(6)` is

A

`969`

B

`970`

C

`971`

D

`972`

Text Solution

Verified by Experts

The correct Answer is:
B
`(3sqrt(3)+sqrt(2))^(6)+(sqrt(3)+sqrt(2))^(6)`
`=2(.^(6)C_(0)(sqrt(3)))^(6)+.^(6)C_(2)(sqrt(3))^(4)(sqrt(2))^(2)+.^(6)C_(4)(sqrt(3))^(2)(sqrt(2))^(4)+.^(6)C_(6)(sqrt(2))^(6))`
`= 970`
Since `0 lt (sqrt(3)-sqrt(2))^(6) lt 1`. The smallest integer larger than `(sqrt(3)+sqrt(2))^(6)` is `970`.
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