Find the value of determinant `|[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[sqrt((15))+sqrt((26)),5,sqrt((10))],[3+sqrt((65)),sqrt((15)),5]|`

Explanation

We have
` Delta=|{:(sqrt(13)+sqrt(3),,2sqrt(5),,sqrt(5)),(sqrt(15)+sqrt(26),,5,,sqrt(10)),(3+ sqrt(65),,sqrt(15),,5):}|`
Taking `sqrt(5)` common from`C_(2) " and " C_(3)` we get
` Delta =(sqrt(5))^(2) |{:(sqrt(13)+sqrt(3),,2,,1),(sqrt(15)+sqrt(26),,sqrt(5),,sqrt(2)),(3+ sqrt(65),,sqrt(3),,sqrt(5)):}|`
Applying `C_(1) to C_(1) -sqrt(3)C_(2) -sqrt(13)C_(3)` we get
`|{:(-sqrt(3),,2,,1),(0,,sqrt(5),,sqrt(2)),(0,,sqrt(3),,sqrt(5)):}|`
(Expanding along `C_(1))`