x square root 2 divided by 3
Answers
Answer:
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
"
Answer link
Related topic
Simplification of Radical Expressions
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