How do you simplify $\sqrt{20} \div \sqrt{15}$ $sqrt 20div sqrt 15$ ?

Question

1702 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-23T20:22:05

$\frac{2 \sqrt{3}}{3}$ $(2sqrt3)/3$

We have the following:

$\frac{\sqrt{20}}{\sqrt{15}}$ $sqrt20/sqrt15$

$20 = 4 \cdot 5$ $20=4*5$ and $15 = 3 \cdot 5$ $15=3*5$ . With this in mind, we can rewrite the radicals in this way. We now have

$\frac{\sqrt{4} \sqrt{5}}{\sqrt{3} \sqrt{5}}$ $(sqrt4sqrt5)/(sqrt3sqrt5)$

Common factors in the numerator and denominator cancel, and we're left with

$(sqrt4cancelsqrt5)/(sqrt3cancelsqrt5)=>2/sqrt3$

The convention is to not have an irrational number in the denominator, so we can multiply this by $sqrt3/sqrt3$ .

We are essentially multiplying by $1$ , and we get

$(2sqrt3)/3$

Hope this helps!

How do you simplify sqrt 20div sqrt 15√20÷√15sqrt 20div sqrt 15?