Question

`(1)/(2) √(48) -5√(147) -\sqrt{108`

Answer 1

`-39√(3)`

Explanation:

Given expression:

`(1)/(2)√(48)-5√(147)-√(108)`

Rewrite 48 as 4²·3, 147 as 7²·3 and 108 as 6²·3:

`\implies (1)/(2)√(4^2 \cdot 3)-5√(7^2 \cdot 3)-√(6^2 \cdot 3)`

`\textsf{Apply radical rule} \quad √(ab)=√(a)√(b):`

`\implies (1)/(2)√(4^2) √(3)-5√(7^2) √(3)-√(6^2) √(3)`

`\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0:`

`\implies (1)/(2)\cdot 4} √(3)-5\cdot7 √(3)-6 √(3)`

Simplify:

`\implies 2 √(3)-35 √(3)-6 √(3)`

Factor out the common term √3:

`\implies (2 -35-6) √(3)`

Carry out the subtraction inside the parentheses:

`\implies -39√(3)`