Question

Rationalize the denominator of 5/√3

Answer 1

5 / sqrt 3 = (5 / sqrt 3)(sqrt 3 / sqrt 3) = 5 sqrt 3 / 3

Answer 2

\[\tt{Rationalising~~the~~denominator}\]_____________________

Any irrational fraction of the form
\[\frac a{\sqrt b}\]
can be rationalised
by multiplying by \(\dfrac{\sqrt b}{\sqrt b}\) (which equals one)

like this
\[\large\frac a{\sqrt b}=\frac a{\sqrt b}\times1\\
\large\qquad=\frac a{\sqrt b}\times\frac{\sqrt b}{\sqrt b}\\
\large\qquad=\frac{a\sqrt b}{b}\]
_____________________

If the irrational fraction of this form
\[\frac \alpha{\beta+\sqrt \gamma }\]

we have to multiply by \(\dfrac {\beta-\sqrt \gamma}{\beta-\sqrt \gamma}\) (which equals one)

\[\large\frac \alpha{\beta+\sqrt \gamma }=\frac \alpha{\beta+\sqrt \gamma }\times\frac {\beta-\sqrt \gamma}{\beta-\sqrt \gamma }\\\,\\\large
\qquad\qquad =\frac{\alpha(\beta-\sqrt\gamma)}{\beta^2-\gamma}\]
_____________________

\(\beta+\sqrt \gamma\) and \(\beta-\sqrt \gamma \) are called irrational conjugates of each other .

Answer 3

5√3/3