Question

√(14)*(3 √(7) + √(32) - √(28) + 2 √(2))

Answer 1

27√2 -2√7 ≈ 32.8923

Explanation:

Apparently, you want to simplify the expression √(14)*(3 √(7) + √(32) - √(28) + 2 √(2)).

Rules of radicals

(√a)(√b) = √(ab)

√(a²b) = a√b

Application

`√(14)\cdot3√(7)+√(32)-√(28)+2√(2)\\\\=3√(14\cdot7)+√(4^2\cdot2)-√(2^2\cdot7)+2√(2)\\\\=3√(7^2\cdot2)+4√(2)-2√(7)+2√(2)=(3\cdot7+4+2)√(2)-2√(7)\\\\=\boxed{27√(2)-2√(7)}`