Question

Which expression is equivalent to sqrt48x^5 if x>0

Answer 1

sqrt (48x^5) if x>0

. implies multiplication

48 = 2. 2.2.2.3= 2^4 .3

sqrt [2^4 .3 (x^5) ] if x>0

sqrt [2^4 ] sqrt [3 ] sqrt [(x^5) ] if x>0

sqrt [16 ] sqrt [3 ] sqrt [(x^5) ] if x>0

4. sqrt [3 ] sqrt [(x^5) ] if x>0

We know, sqrt [(x^5) ] if x>0 = x^2. sqrt [(x) ]

4. sqrt [3 ] .x^2. sqrt [(x) ] if x>0

4x^2 sqrt[3x] (answer c)

Explanation:

Answer 2

sqrt 48 = sqrt 16 . 3
sqrt 48 = 4 sqrt 3

sqrt (x^5) = sqrt x^4 . sqrt x
= (x^4)^1/2 . sqrt x
= x^2 . sqrt x

= 4 . sqrt 3 . x^2 . sqrt x
= 4x^2 sqrt 3x (C)