Question

Which expression is equivalent to √2x^5/18? Assume x > 0.

Answer 1

Answer: $\frac{x^2\sqrt{x}}{3}$

Step-by-step explanation:

Here the given expression is, $\sqrt{\frac{2x^5}{18} }$

= $\sqrt{\frac{x^5}{9} }$

= $\sqrt{\frac{x^5}{9} }$

= $\sqrt{\frac{x^4.x^1}{9} }$  (because $x^{m+n}= x^m.x^n$ )

=$\frac{x^2\sqrt{x} }{3}$

Thus,$\sqrt{\frac{2x^5}{18} }$ =$\frac{x^2\sqrt{x} }{3}$

Answer 2

$\sqrt{\dfrac{2x^5}{18}}=\sqrt{\dfrac{2}{18}\cdot x^2\cdot x^2\cdot x}=\sqrt{\dfrac{1}{9}\cdot x^2\cdot x^2\cdot x}=\sqrt{\dfrac{1}{9}}\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{x}=\\\\\\=\dfrac{1}{3}\cdot x\cdot x\cdot\sqrt{x}=\boxed{\dfrac{x^2\sqrt{x}}{3}}$

Answer A.