443,470 views
31 votes
31 votes
Express with radical signs instead of fractional exponents. Rationalize the dominator.

Express with radical signs instead of fractional exponents. Rationalize the dominator-example-1
User Linakis
by
2.2k points

1 Answer

15 votes
15 votes

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)

User Clowwindy
by
3.0k points