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

1 Answer
May 27, 2016

Answer:

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

Explanation:

#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) #