Question #6766a

1 Answer
sente
Oct 13, 2016

Show that

(4sqrt(5)-3sqrt(2))^2=98-sqrt(10)

Explanation:

Using that (a-b)^2 = a^2-2ab+b^2, and sqrt(a)sqrt(b) = sqrt(ab) for a, b >=0, we have

(4sqrt(5)-3sqrt(2))^2 = (4sqrt(5))^2-2(4sqrt(5))(3sqrt(2))+(3sqrt(2))^2

=4^2(sqrt(5))^2-24sqrt(5)sqrt(2)+3^2(sqrt(2))^2

=16(5)-24sqrt(5*2)+9*2

=98-24sqrt(10)

Related questions
See all questions in Square Roots and Irrational Numbers
Impact of this question
1463 views around the world
You can reuse this answer
Creative Commons License