# If the expression (3^d*sqrt5)/(3^2*sqrt45) is equal to 3, what is the value of d?

Dec 16, 2016

$4$

#### Explanation:

Set up as an equation:

$\frac{{3}^{d} \cdot \sqrt{5}}{{3}^{2} \cdot \sqrt{9 \times 5}} = 3$

$\frac{{3}^{d} \cdot \sqrt{5}}{9 \cdot 3 \sqrt{5}} = 3$

$\frac{{3}^{d} \cdot \sqrt{5}}{27 \sqrt{5}} = 3$

${3}^{d} \cdot \sqrt{5} = 81 \sqrt{5}$

${3}^{d} = 81$

${3}^{d} = {3}^{4}$

$d = 4$

Hopefully this helps!