Equivalent expressions are expressions with equal values
The equivalent expression of [tex]\sqrt{\frac{2x^5}{18}}[/tex]is [tex]\frac{x^2\sqrt{ x}}{3}[/tex]
The expression is given as:
[tex]\sqrt{\frac{2x^5}{18}}[/tex]
Divide 2 and 18, by 2
[tex]\sqrt{\frac{2x^5}{18}} = \sqrt{\frac{x^5}{9}}[/tex]
Take the square root of 9
[tex]\sqrt{\frac{2x^5}{18}} = \frac{\sqrt{x^5}}{3}[/tex]
Expand x^5 as x^4 * x
[tex]\sqrt{\frac{2x^5}{18}} = \frac{\sqrt{x^4 * x}}{3}[/tex]
Take the square root of x^4
[tex]\sqrt{\frac{2x^5}{18}} = x^2\frac{\sqrt{ x}}{3}[/tex]
Rewrite as:
[tex]\sqrt{\frac{2x^5}{18}} = \frac{x^2\sqrt{ x}}{3}[/tex]
Hence, the equivalent expression of [tex]\sqrt{\frac{2x^5}{18}}[/tex]is [tex]\frac{x^2\sqrt{ x}}{3}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
