How do you multiply (sqrt3+ 2sqrt5)^2?

1 Answer
Alan P.
Jul 5, 2015

(sqrt(3)+2sqrt(5))^2
color(white)("XXXX")

Explanation:

(sqrt(3)+2sqrt(5))^2
color(white)("XXXX")=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)+2sqrt(5)))

color(white)("XXXX")=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)))+color(red)((sqrt(3)+2sqrt(5)))*color(blue)((2sqrt(5))

color(white)("XXXX")= color(red)((sqrt(3)))*color(blue)((sqrt(3))) +color(red)((2sqrt(5))*color(blue)((sqrt(3)))+color(red)((sqrt(3))*color(blue)((2sqrt(5)))+color(red)((2sqrt(5)))*color(blue)((2sqrt(5)))

color(white)("XXXX")= 3 + 2sqrt(15) + 2sqrt(15) + 20

color(white)("XXXX")=23 + 4sqrt(15)

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1667 views around the world
You can reuse this answer
Creative Commons License