What is the exact value of the expression √294 - √24 + √54

That simplifies to 8 √ 6
= 19.5959179422654...

sqrt(294) - sqrt(24) + sqrt(54)
= sqrt(49 * 6) - sqrt(4 * 6) + sqrt(9 * 6)
= sqrt(49)*sqrt(6) - sqrt(4)*sqrt(6) + sqrt(9)*sqrt(6)
= 7*sqrt(6) - 2*sqrt(6) + 3*sqrt(6)
= (7 - 2 + 3)*sqrt(6)
= 8*sqrt(6)
= sqrt(64)*sqrt(6)
= sqrt(384)