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secondary 3 | A Maths
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Benjay
Benjay

secondary 3 chevron_right A Maths chevron_right Singapore

need help thanks!

Date Posted: 2 years ago
Views: 445
J
J
2 years ago
(√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)

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Johnson
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