Question

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

Answer 1

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. `\sqrt{a \cdot b}=\sqrt{a}\cdot\sqrt{b}`

Since `15=3\cdot5` and `20=2^2 \cdot 5`, you have that

`\frac{\sqrt{15}}{15\sqrt{20}} = \frac{\sqrt{3\cdot5}}{15\sqrt{2^2 \cdot 5}}`

For what we said above, this equals

`\frac{\sqrt{3}\sqrt{5}}{15\sqrt{2^2}\sqrt{5}}`

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

`\sqrt{3} / 30`