To rationalize the denominator of the expression 23

Question

smallq9 · Accepted Answer

Step 1
The denominator of a rational expression can be rationalized by removing the irrational term from it.
To remove the irrational term, the numerator and denominator of the expression are multiplied by the conjugate of the denominator.
Conjugate of an expression

\sqrt{a} + \sqrt{b}

is given as

\sqrt{a} - \sqrt{b}

and vice-versa.
Given expression is

\frac{2}{\sqrt{3}}

This can be written as:

\frac{2}{\sqrt{3} + 0}

So the conjugate of the denominator is given as

\sqrt{3} - 0 = \sqrt{3}

Multiplying the numerator and the denominator with the conjugate,

\frac{2}{\sqrt{3}} = \frac{2 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}

\frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{{(s q e r {3})}^{2}}

\frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3}

(Since square and square root are opposite operations, they cancel out).

To rationalize the denominator of the expression \frac{2}{\sqrt{3}}

Answered question

Answer & Explanation

New Questions in Algebra II