How do you simplify sqrt 5(sqrt 2+sqrt 10)?

1 Answer
Pythagoras
Sep 25, 2015

sqrt(10)(1+sqrt(5)) or sqrt(2)(sqrt(5)+5)

Explanation:

sqrt(5)(sqrt(2)+sqrt(10))
=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)
=sqrt(5*2)+sqrt(5)*sqrt(10)
=sqrt(10)+sqrt(5)*sqrt(10)
=sqrt(10)(1+sqrt(5))

or

sqrt(5)(sqrt(2)+sqrt(10))
=sqrt(5)*sqrt(2)+sqrt(5)*sqrt(10)
=sqrt(5)*sqrt(2)+sqrt(5*10)
=sqrt(5)*sqrt(2)+sqrt(50)
=sqrt(5)*sqrt(2)+sqrt(2*25)
=sqrt(5)*sqrt(2)+sqrt(2)*sqrt(25)
=sqrt(5)*sqrt(2)+5sqrt(2)
=sqrt(2)(sqrt(5)+5)

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
7553 views around the world
You can reuse this answer
Creative Commons License