# How do you simplify sqrt(15)/(15sqrt(20))?

Feb 4, 2015

You could factor the number in primes, and use the fact that the square root of a multiplication is the product of the square roots, i.e. $\setminus \sqrt{a \setminus \cdot b} = \setminus \sqrt{a} \setminus \cdot \setminus \sqrt{b}$

Since $15 = 3 \setminus \cdot 5$ and $20 = {2}^{2} \setminus \cdot 5$, you have that

$\setminus \frac{\setminus \sqrt{15}}{15 \setminus \sqrt{20}} = \setminus \frac{\setminus \sqrt{3 \setminus \cdot 5}}{15 \setminus \sqrt{{2}^{2} \setminus \cdot 5}}$

For what we said above, this equals

$\setminus \frac{\setminus \sqrt{3} \setminus \sqrt{5}}{15 \setminus \sqrt{{2}^{2}} \setminus \sqrt{5}}$

So, we can simplify $\setminus \sqrt{5}$, and use the fact that $\setminus \sqrt{{2}^{2}} = 2$ to write

$\setminus \frac{\sqrt{3}}{30}$