Question

simplifying radicals √3 ÷ √6

Answer 1

So we can write the following:\[\frac{ \sqrt 3 }{ \sqrt 6 } = \sqrt \frac{ 3 }{ 6 }\]And then simplify the inside. What do you get?

Answer 2

um .5

Answer 3

Right, but for now we'll keep it as 1/2. So then that's\[\sqrt \frac{ 1 }{ 2 } = \frac{ \sqrt 1 }{ \sqrt 2 } = \frac{ 1 }{ \sqrt 2 } = \frac{ \sqrt 2 }{ 2 }\]Do you get it?

Answer 4

not really

Answer 5

What part don't you understand?

Answer 6

why did you take off the √ of 1 then it went to √2/ 2

Answer 7

Let's take it piece by piece. For the first part, what's the square root of 1?

Answer 8

1

Answer 9

Right. So we can essentially just take off the square root. Good?

Answer 10

yes

Answer 11

Great. So now for the second part - that's called rationalizing. Mathematicians don't like square roots in the denominator of fractions, so we do the following:\[\frac{ 1 }{ \sqrt 2 } = \frac{ 1 }{ \sqrt 2} \times \frac{ \sqrt 2 }{ \sqrt 2 } = \frac{ \sqrt 2 }{ \sqrt 2 \times \sqrt 2 } = \frac{ \sqrt 2 }{ 2 }\]Does that make sense now?