Question

Simplify:
$4\sqrt{3}(2\sqrt{27}-4\sqrt{48})-5\sqrt{3}(\sqrt{12}-3\sqrt{75})$.

• A. 75
• B. 48
• C. 78
• D. 57

Answer 1

The correct option is A 75

Given $4\sqrt{3}(2\sqrt{27}-4\sqrt{48})-5\sqrt{3}(\sqrt{12}-3\sqrt{75})$
$=4\sqrt{3}(2\sqrt{3\times 3\times 3}-4\sqrt{4\times 4\times 3})-5\sqrt{3}(\sqrt{2\times 2\times 3}-3\sqrt{5\times 5\times 3})$ [Since, $\sqrt{a\times a}=a$]
$=4\sqrt{3}(2\times 3\sqrt{3}-4\times 4\sqrt{3})-5\sqrt{3}(2\sqrt{3}-3\times 5\sqrt{3})$
$=4\sqrt{3}(6\sqrt{3}-16\sqrt{3})-5\sqrt{3}(2\sqrt{3}-15\sqrt{3})$
$=4\sqrt{3}(-10\sqrt{3})-5\sqrt{3}(-13\sqrt{3})$
$=-40\sqrt{3\times 3}+65\sqrt{3\times 3}$
$=-40\times 3+65\times 3=-120+195=75$ is the value of the given expression.