Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 3 | A Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
need help thanks!
Date Posted: 2 years ago
Views: 402
(√a - √b)²
= (√a)² - 2 √a √b + (√b)²
(recall the property (a - b)² = a² - 2ab + b²)
= a - 2√ab + b
= a + b - 2√ab
So,
√a - √b = √(a + b - 2√ab)
Note that since a > b > 0,
√a > √b > 0
For example, 5 > 4
√5 > √4
So, √a - √b > 0
We have to take the positive square root of (a + b - 2√ab) and not the negative square root.
If you were asked for √b - √a instead, it would equal -√(a + b + √ab)
= (√a)² - 2 √a √b + (√b)²
(recall the property (a - b)² = a² - 2ab + b²)
= a - 2√ab + b
= a + b - 2√ab
So,
√a - √b = √(a + b - 2√ab)
Note that since a > b > 0,
√a > √b > 0
For example, 5 > 4
√5 > √4
So, √a - √b > 0
We have to take the positive square root of (a + b - 2√ab) and not the negative square root.
If you were asked for √b - √a instead, it would equal -√(a + b + √ab)
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Hope u find it useful
Date Posted:
2 years ago
360 Tutoring Program