Question

If $x>0$, which is equal to $\sqrt{x^3}$?

What is possible value of x

$\left(i\right)x+x^{\frac{1}{2}}\left(ii\right)\left(x^{\frac{1}{2}}{)}^3\right(iii\left)\right(x^2\left)\right(x{)}^{\frac{-1}{2}}$

• A. (ii) and (iii) only
• B. (i) and (ii) only
• C. (i) and (iii) only
• D. (i), (ii) and (iii)

Answer 1

The correct option is A (ii) and (iii) only

$Now\sqrt{x^3}={\left(x^3\right)}^{\frac{1}{2}}=x^{\frac{3}{2}}={\left(x^{\frac{1}{2}}\right)}^3=option\left(ii\right)Alsooption\left(iii\right)=\left(x^2\right){\left(x\right)}^{-\frac{1}{2}}=x^{2-\frac{1}{2}}=x^{\frac{3}{2}}$