Question

Simplify
(6√2+2√3)(√10-4√7)

Answer 1

Answer:

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

Or

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

Step-by-step 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:

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

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

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

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

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

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

$\tt \: = 12√5−24√(14)+2√(30)−8√(21)$

or

$\tt \: \approx88.7$

$\rule{230pt}{2pt}$

Answer 2

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

$=12\sqrt{5} -24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\\approx -88.68$