Question

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

Answer 1

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 {(2x^5)/(18)}\\\\=\sqrt{(x^5)/(9)}\\\\=(x^2)/(3)*√(x)`

This can be illustrated by

Original Expression

`A=\sqrt {(2x^5)/(18)}\\\\ \text{put, x=1}\\\\A=\sqrt{(2 * 1^5)/(18)}\\\\A=\sqrt{(1)/(9)}\\\\A=(1)/(3)\\\\\text{Equivalent Expression B}\rightarrow (x^2)/(3)* √(x)\\\\\text{put,x=1}\\\\B=(1^2)/(3)* √(1)\\\\B=(1)/(3)`

Answer 2

Assume x > 0

√(2x⁵/18)

= √(2/18) * √(x⁵)

= √(1/9) * √(x⁴ · x)

= 1/3 * √x⁴ * √x

= 1/3 * x² * √x

= 1/3 * x²√x

=
`( x^(2) √(x) )/(3)`