Answer
$7 \sqrt {2}$
Work Step by Step
First, we rewrite the problem in the form of a fraction:
$28 \div \sqrt {8} = \frac{28}{\sqrt 8}$
Let's look at the denominator. We can rewrite $8$ as the product of a perfect square and another factor. $8$ can be rewritten as $4 • 2$:
$\frac{28}{\sqrt {4 • 2}}$
Take the square root of $4$:
$\frac{28}{2 \sqrt {2}}$
Divide both the numerator and the denominator by their greatest common factor, $2$:
$\frac{14}{\sqrt {2}}$
We do not like to leave radicals in the denominator. To get rid of the radical in the denominator, we multiply both the numerator and denominator by $\sqrt {2}$:
$\frac{14 \sqrt {2}}{2}$
Divide the numerator and denominator by their greatest common factor, $2$:
$7 \sqrt {2}$
