Question

Evaluate (root5+root2)^2+(root8-root5)^2

Answer 1

2(10 - √10) or 13.68 to the nearest hundredth.

Explanation:

(√5 + √2)^2 + (√8 - √5)^2

= 5 + 2 + 2√5√2 + (8 + 5 - 2√8√5)

= 7 + 2√10 + 13 - 2√40

= 20 + 2√10 - 2√40

= 20 + 2√10 - 4√10

= 20 - 2√10

= 2(10 - √10).