How do you simplify #(5sqrt2+3sqrt5)(2sqrt10-5)#?

2 Answers
Mar 24, 2017

Answer:

#=5(sqrt5 +sqrt2)#

Explanation:

You can multiply the brackets using the distributive law, in exactly the same way as in cases such as:

#(x+3)(x-4) = x^2 -4x +3x-12#

Each term in the first bracket must be multiplied by each term is the second bracket.

#(color(red)(5sqrt2) +color(blue)(3sqrt5))(2sqrt10-5)#

#=color(red)(5sqrt2)(2sqrt10-5) +color(blue)(3sqrt5)(2sqrt10-5)#

#=10sqrt20-25sqrt2+6sqrt50-15sqrt5#

Now find factors for the roots, using squares where possible:

#=10sqrt(color(magenta)(4)xx5)-25sqrt2+6sqrt((color(lime)25xx2)-15sqrt5#

#=10xxcolor(magenta)(2)sqrt5-25sqrt2+6 xxcolor(lime)5sqrt2 -15sqrt5#

#=20sqrt5 -15sqrt5+30sqrt2-25sqrt2#

#=5sqrt5+5sqrt2#

#=5(sqrt5 +sqrt2)#

Mar 24, 2017

Answer:

#5(sqrt2+sqrt5)#

Explanation:

#(5sqrt2+3sqrt5)(2sqrt10-5)#

#color(white)(aaaaaaaaaaaaa)##5sqrt2+3sqrt5#
#color(white)(aaaaaaaaaaaaa)##2sqrt10-5#
#color(white)(aaaaaaaaaaaaa)##-----#
#color(white)(aaaaaaaaaaaaa)##10sqrt2sqrt10+6sqrt5sqrt10#
#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)##-25sqrt2-15sqrt5#
#color(white)(aaaaaaaaaaaaa)##-------------#
#color(white)(aaaaaaaaaaaa)##color(blue)(10sqrt2sqrt10+6sqrt5sqrt10-25sqrt2-15sqrt5#

#:.=10sqrt2 xx sqrt2 xx sqrt5+6sqrt5 xx sqrt2 xx sqrt5-25sqrt2-15sqrt5#

#:.=10 xx 2sqrt5+6 xx 5 xx sqrt2-25sqrt2-15sqrt5#

#:.=20sqrt5+30sqrt2-25sqrt2-15sqrt5#

#:.=20sqrt5-15sqrt5+30sqrt2-25sqrt2#

#:.=5sqrt5+5sqrt2#

#:.color(blue)(=5(sqrt2+sqrt5)#