Answer
$\frac{d\sqrt {21}}{3}$
Work Step by Step
First, we need to cancel out common terms in the numerator and denominator:
$\sqrt {\frac{7d^2}{3}}$
Separate the radical:
$\frac{\sqrt {7d^2}}{\sqrt {3}}$
Take the square root of any perfect squares:
$\frac{d\sqrt {7}}{\sqrt {3}}$
We don't want to leave radicals in the denominator, so to get rid of radicals in the denominator, we multiply both the numerator and denominator by the denominator:
$\frac{d\sqrt {7}}{\sqrt {3}} • \frac{\sqrt {3}}{\sqrt {3}}$
Multiply to simplify:
$\frac{d\sqrt {21}}{\sqrt {9}}$
Take the square root of any perfect squares:
$\frac{d\sqrt {21}}{3}$
