How do you simplify $5 sqrt10 times 2 sqrt8$ ?

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Answer 1 · 2016-05-27T14:48:56

$= color(green)( 40sqrt ( 5)$

$5 sqrt10 xx 2 sqrt8$

$= 5 xx sqrt10 xx 2 xx color(green)(sqrt8$

Simplifying $color(green)(sqrt8$ by prime factorising $8$ :(expressing $8$ as a product of its prime factors)

$= 5 xx sqrt10 xx 2 xx color(green)(sqrt (2 * 2 * 2)$

$= 5 xx sqrt10 xx 2 xx color(green)(sqrt (2 ^2* 2)$

$= 5 xx sqrt10 xx 2 xx color(green)(2sqrt (2)$

$= 5 xx 2 xx 2 xx sqrt10 xx sqrt (2)$

$= 20 sqrt (color(blue)(10) xx 2)$

$= 20 sqrt (color(blue)(5 xx 2) xx 2)$

$= 20 sqrt ( 5 xx 2^2)$

$= 20 xx 2 sqrt ( 5)$

$= 40sqrt ( 5)$

How do you simplify 5 sqrt10 times 2 sqrt85 sqrt10 times 2 sqrt8?