Question

a/(4√(ab))Rationalize the denominator:-

Answer 1

Given the expression:

$\frac{a}{4\sqrt{ab}}$

You can rationalize the denominator by multiplying the numerator and the denominator by the square root in the denominator. Set up that:

$=\frac{a}{4\sqrt{ab}}\cdot\frac{\sqrt{ab}}{\sqrt{ab}}$

Remember the following Property for Radicals:

$(\sqrt{x})(\sqrt{x})=(\sqrt{x})^2=x$

Then, you get:

$=\frac{a\sqrt{ab}}{4(\sqrt{ab)^2}}$$=\frac{a\sqrt{ab}}{4ab}$

Notice that there is an "a" in the numerator and in the numerator. Knowing that:

$\frac{a}{a}=1$

You get:

$=\frac{\sqrt{ab}}{4b}$

Hence, the answer is:

$=\frac{\sqrt{ab}}{4b}$