How do you multiply #(sqrt5-sqrt6)(sqrt5+sqrt2)#?

1 Answer
May 19, 2018

Answer:

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(sqrt(5)) - color(red)(sqrt(6)))(color(blue)(sqrt(5)) + color(blue)(sqrt(2)))# becomes:

#(color(red)(sqrt(5)) xx color(blue)(sqrt(5))) + (color(red)(sqrt(5)) xx color(blue)(sqrt(2))) - (color(red)(sqrt(6)) xx color(blue)(sqrt(5))) - (color(red)(sqrt(6)) xx color(blue)(sqrt(2)))#

We can now use this rule for radicals to multiply the radicals:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#sqrt(color(red)(5) xx color(blue)(5)) + sqrt(color(red)(5) xx color(blue)(2)) - sqrt(color(red)(6) xx color(blue)(5)) - sqrt(color(red)(6) xx color(blue)(2))#

#sqrt(25) + sqrt(10) - sqrt(30) - sqrt(12)#

#5 + sqrt(10) - sqrt(30) - sqrt(12)#

We can then use this rule for radicals to simplify the term on the right:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#5 + sqrt(10) - sqrt(30) - sqrt(12)#

#5 + sqrt(10) - sqrt(30) - sqrt(color(red)(4) * color(blue)(3))#

#5 + sqrt(10) - sqrt(30) - (sqrt(color(red)(4)) * sqrt(color(blue)(3)))#

#5 + sqrt(10) - sqrt(30) - 2sqrt(3)#