Question

Упростите выражение
(√10+√5)×√20×5√8 ​

Answer 1

Ответ:

$200 + 100 \sqrt{2}$

Объяснение:

$( \sqrt{10} + \sqrt{5} ) \times \sqrt{20} \times \\ \times 5 \sqrt{8} = \\ = ( \sqrt{10} + \sqrt{5} ) \times \sqrt{25 \times 20 \times 8} = \\ = ( \sqrt{10} + \sqrt{5} ) \times \sqrt{4000} = \\ = \sqrt{4000} \times ( \sqrt{10} + \sqrt{5} ) = \\ = 20 \sqrt{10} \times ( \sqrt{10} + \sqrt{5} ) = \\ = 20 \sqrt{10} \times \sqrt{10} + 20 \sqrt{10} \times \sqrt{5} = \\ = 20 \times 10 + 20 \sqrt{10 \times 5} = \\ = 200 + 20 \sqrt{50} = \\ = 200 + 20 \sqrt{25 \times 2} = \\ = 200 + 20 \times 5 \sqrt{2} = \\ = 200 + 100 \sqrt{2}$