Question

(1/2^1/2)^2=
that is square root of one over 2 square is (1/2^1/2)^2=
that is square root of one over 2 square is @Mathematics

Answer 1

\[\frac{1}{2}\]

Answer 2

but it should be 1/4

Answer 3

\[\frac{\sqrt{1}}{2^2}\]
Is that your question? what you said and what you typed are rather different.

Answer 4

is this your question - what is the square root of:\[\frac{1}{2^2}\]

Answer 5

or is it this - what is the square root of:\[(\frac{1}{\sqrt{2}})^2\]

Answer 6

yeah asnaseer the 2nd one

Answer 7

If it should be 1/4 I assume its:
\[\frac{\sqrt{1}}{2^2}=\frac{1}{4}\]
sqrt 1 = 1
2^2 = 4
Of course, it could be:
\[(\frac{\sqrt 1}{2})^2=(\frac{1}{2})^2=\frac{1}{4}\]

Answer 8

(1/(sqrt 2))^2 = 1/2
which fails the previous condition you gave that it needs to be 1/4
and
sqrt (1/(sqrt 2))^2 = 1/(sqrt 2)

Answer 9

in that case just remember that square root is the inverse of square (with a plus/minus of course), i.e.:\[\sqrt{x^2}=\pm x\]so:\[\sqrt{(\frac{1}{\sqrt{2}})^2}=\pm\frac{1}{\sqrt{2}}\]

Answer 10

because:\[x*x=x^2\]and:\[(-x)*(-x)=x^2\]

Answer 11

i mean 1 divided by square root of all squared

Answer 12

??

Answer 13

i divided by square root of 2 all squared

Answer 14

\[\sqrt{\frac{1}{2}}^2=\frac{1}{2}\]

Answer 15

NO!!!!!!!!! 1 DIvided by square root of 2 then all squared

Answer 16

\[(\frac{1}{\sqrt{2}})^2=\frac{1}{2}\] if you prefer

Answer 17

same thing since
\[\sqrt{\frac{1}{2}}=\frac{\sqrt{1}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\]

Answer 18

ok, in that case:\[(\frac{1}{\sqrt{2}})^2=\frac{1}{\sqrt{2}}*\frac{1}{\sqrt{2}}=\frac{1*1}{\sqrt{2}*\sqrt{2}}=\frac{1}{2}\]

Answer 19

yeah that one

Answer 20

but why should it be 1/2?

Answer 21

if the square roots cancel out,it should be 1/4

Answer 22

are you familiar with the rules for indexes? i.e. do you know:\[a^n*a^m=a^{n+m}\]

Answer 23

yeah i do

Answer 24

if you do, then you could re-write:\[\sqrt{2}=2^{0.5}\]so that:\[\sqrt{2}*\sqrt{2}=2^{0.5}*2^{0.5}=2^{0.5+0.5}=2^1=2\]

Answer 25

@krypton - do you understand now?

Answer 26

yeah i now do thanks

Answer 27

no problem - glad to help

Answer 28

actually what you really need is that given any positive number, the square of the square root is that number. the square root means "the number whose square is given" so for example
\[\sqrt{25}=5\iff 5^2=25\]
therefore it is always true that for any positive number
\[\sqrt{a}^2=a\]

Answer 29

wolfram alpha people wolfram alpha