Question

The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to ______.

Answer 1

The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to 0.

Explanation:

Taking `sqrt(5)` common from C₂ and C₃ and applying `"C"_1 -> "C"_3 - sqrt(3)` C₂, we get the desired result.