Question

Which expression is equivalent to square root of 2x^5/18? Assume

Answer 1

Assume x > 0

√(2x⁵/18)

= √(2/18) * √(x⁵)

= √(1/9) * √(x⁴ · x)

= 1/3 * √x⁴ * √x

= 1/3 * x² * √x

= 1/3 * x²√x

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

Answer 2

Answer with explanation:

The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.

The expression which is equivalent to:

$\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}$

This can be illustrated by

Original Expression

$A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}$