Question

Simplify
(6√2+2√3)(√10-4√7)

Answer 1

`\boxed{\tt = 1 2√5−24√(14)+2√(30)−8√(21)}`

Or

`\boxed{ \tt \approx88.7}`

Explanation:

Apply FOIL method to expand:

`=\tt6√2(√(10)−4√7)+2√3(√(10)−4√7)`

`\tt \:=6√2√(10)+6√2(−4√7)+2√3(√(10)−4√7)`

`\tt \: = 6√2√(10)+6√2(−4√7)+2√3√10+2√3(−4√7)`

Simplify:

`=\tt6√(20)+6√2(−4√7)+2√3√(10)+2√3(−4√7)`

`\tt \: = 6 \sqrt{2 {}^(2) * 5} +6√2(−4√7)+2√3√(10)+2√3(−4√7)`

`\tt \: = 6(2√5)+6√2(−4√7)+2√3√(10)+2√3(−4√7)`

`\tt = 12√5+6√2(−4√7)+2√3√(10)+2√3(−4√7)`

`\tt = 12√5−24√(14)+2√3√(10)+2√3(−4√7)`

`\tt \: = 12√5−24√14+2√(30)+2√3(−4√7)`

`\tt \: = 12√5−24√(14)+2√(30)−8√(21)`

or

`\tt \: \approx88.7`

`\rule{230pt}{2pt}`

Answer 2

`\left( 6 \sqrt 2 + 2 \sqrt 3 \right) \left( √(10) -4 \sqrt7 \right)\\\\=\left(6\sqrt 2 \right) \left(√(10) \right) - \left(6\sqrt 2\right)\left(4\sqrt 7 \right)+\left(2\sqrt 3 \right) \left(√(10) \right)-\left(2\sqrt 3 \right) \left(4 \sqrt 7 \right)\\\\=6√(2 \cdot 10) -24√(2 \cdot 7) + 2√(10 \cdot 3) - 8 √(3 \cdot 7)\\\\=6√(4 \cdot 5)-24√(14)+2√(30) - 8 √(21)\\\\=6\cdot 2\sqrt 5-24√(14)+2√(30) - 8 √(21)\\\\`

`=12√(5) -24√(14)+2√(30) - 8 √(21)\\\\\approx -88.68`