The complexity is strong with this one

Algebra Level 2

Is a × b \sqrt a \times \sqrt b always equal to a b \sqrt{ab} ?

No Yes

Akshay Sreenivasan by Akshay Sreenivasan , 23, India

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2 solutions

Johnny Jillky
Mar 20, 2016

− 1 × − 1 = i × i = − 1 ≠ − 1 × − 1 = 1 \sqrt{-1} \times \sqrt{-1} = i \times i = -1 \neq \sqrt{-1 \times -1} = 1

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I f a , b ∈ ( − ∞ , 0 ) , t h i s d o e s n o t h o l d t r u e . E x a m p l e a = − 3 , b = − 1 − 3 × − 1 = 3 i × 1 i = 3 i 2 = − 3 If\quad a,b\in (-\infty ,0),\quad this\quad does\quad not\quad hold\quad true.\\ Example\quad a=-3\quad ,\quad b=-1\\ \sqrt { -3 } \quad \times \quad \sqrt { -1 } \quad =\quad \sqrt { 3 } i\quad \times \quad \sqrt { 1 } i\quad =\quad \sqrt { 3 } { i }^{ 2 }\quad =\quad -\sqrt { 3 }

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