Simplify by expressing with radicals. 3 divided square root of 3=

Step-by-step explanation:

"the square root of

3

divided by

2

" could mean either of the following:

√

3

2

"the square root of:

3

divided by

2

"

√

3

2

"the square root of

3

, divided by

2

".

A square root of a number

n

is a number

x

, such that

x

2

=

n

. Every non-zero number actually has two square roots, which we call

√

n

and

−

√

n

. When we say "the" square root, we usually mean the principal one

√

n

, which for

n

≥

0

is the non-negative one.

In either of the above interpretations of the question, the resulting number will be an irrational number - not a rational one.

Considering each in turn:

We can "simplify" the first square root

Note that if

a

,

b

>

0

then

√

a

b

=

√

a

√

b

, so...

√

3

2

=

√

6

4

=

√

6

2

2

=

√

6

√

2

2

=

√

6

2

We have:

√

3

2

=

√

6

2

≈

1.2247

The second expression cannot be simplified in that way:

√

3

2

is in simplest form.

As an approximation, we can write:

√

3

2

≈

0.8660

This particular number is important as it occurs as the height of an equilateral triangle with sides of length

1

. More commonly, to separate out the divisor

2

, we consider an equilateral triangle of side

2

and bisect it...

enter image source here

Hence we find that:

sin

(

π

3

)

=

cos

(

π

6

)

=

√

3

2

So when you encountered the expression "the square root of

3

divided by

2

" it seems likely to me that the intention was:

"the square root of

3

, divided by

2

"

that's your answer mate sorry for wrote this type of

n

step-by-step explanation: