How do you simplify $(6 sqrt 5) div (5 sqrt 3)$ ?

Question

2058 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-05T16:21:30

$(2sqrt15)/5$

To simplify

$=(6sqrt5)/(5sqrt3)$

We should "rationalize" the denominator. This means, try to get the $sqrt3$ out of the denominator.

We can do this by multiplying the fraction by $sqrt3/sqrt3$ .

$=(6sqrt5)/(5sqrt3)(sqrt3/sqrt3)$

In the numerator, we use the rule that $sqrtasqrtb=sqrt(ab)$ , so $sqrt5sqrt3=sqrt15$ .

In the denominator, we see that $sqrt3sqrt3=3$ , so the square root has been eliminated from the denominator.

$=(6sqrt15)/(5*3)$

Simplify the fraction:

$=(2sqrt15)/5$

How do you simplify (6 sqrt 5) div (5 sqrt 3)(6 sqrt 5) div (5 sqrt 3)?