Question

Express with radical signs instead of fractional exponents. Rationalize the dominator.

Answer 1

Given:

`3^{-(1)/(2)}.x^{(1)/(2)}`

To find:

Express with radical signs instead of fractional exponents. also, rationalize the denominator.

Step-by-step explanation:

The radical sign is a symbol used to indicate a root, i.e.,

`\sqrt[n]{x}`

For our given expression, we can write it using the radical sign as given below:

`\begin{gathered} \frac{x^{(1)/(2)}}{3^{(1)/(2)}} \\ \Rightarrow(√(x))/(√(3)) \end{gathered}`

Now, to rationalize, the following form can be used,

`(√(a))/(√(b))=(√(a))/(√(b))((√(b))/(√(b)))=(√(ab))/(b)`

So, we can also rewrite our expression to rationalize the denominator,

`(√(x))/(√(3))=(√(x))/(√(3))*((√(3))/(√(3)))=(√(3x))/(3)`

Final answer:

The required expression with radical signs and simplified form is as given below:

`(√(3x))/(3)`