How do you simplify #sqrt5(10-4sqrt2)#?

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Answer 1 · 2016-06-19T07:37:25

# = color(green)(10sqrt5 - 4 sqrt 10#

#sqrt5 (10 - 4sqrt2)#

# = color(blue)(sqrt5) * (10 - 4sqrt2)#

We multiply #color(blue)(sqrt5# with each of the two terms within brackets.

# = color(blue)(sqrt5) * (10 ) + color(blue)(sqrt5) * ( - 4sqrt2)#

# = 10sqrt5 + (- 4) * sqrt2 * sqrt5#

# = 10sqrt5 - 4 * sqrt (2 * 5)#

# = 10sqrt5 - 4 sqrt 10#